State  Board 
Examinations 

Questions  and  Answ^ers 

By  C.  HENRY  BROWN,  M.  D. 

Formerly  Physician  Philadelphia  Hospitals- 
Professor  Principles  and  Practice  of  Op- 
tometry; Author  the  Optician's  Manual, 
Vols.  I  and  II;  Clinics  in   Optometry,  Etc. 


19  19 


The  keystone  publishing  Co. 

PHILADELPHIA,  U.      S.      A. 


/  3  >  I 

OPTOMETRY 


COPYRIGHT,  I9I9,  BY 
THE   KEYSTONE  PUBLISHING   CO. 


cpr& 


Preface 


The  one  thousand  questions  answered  in  this  volume  were 
carefully  selected  from  the  examination  papers  set  by  the  State 
Boards  of  Examiners  in  Optometry.  The  book  was  compiled  to 
meet  the  needs  of  those  who  may  find  it  compulsory  or  advisable 
to  take  a  State  Board  examination,  and  for  optometry  students 
generally. 

The  questions  are  probably  more  fully  answered  than  a 
State  examining  board  would  expect,  the  idea  being  to  give  com- 
plete information  on  the  special  subject  brought  out  by  each 
question. 

The  contents  are  classified  under  different  headings,  which 
gives  the  work  the  character  of  a  text-book  and  facilitates  study 
and  reference.  As  the  questions  were  selected  with  a  view  to 
avoiding  repetition,  the  book  will  be  found  to  cover  thoroughly 
every  paper  set  by  any  of  the  State  Examining  Boards. 


Contents 


Theoretic  Optics 9 

Practical  Optics 97 

Theoretic  Optometry 137 

Practical  Optometry 174 

Pathological  Optometry 218 

Physiological  Optics 236 

Anatomy  of  the  Eye 272 

Ophthalmoscopy 283 

Retinoscopy 293 

Physiology  of  Vision 321 

Pathological  Conditions : 346 


Theoretic  Optics 

A  coin  one  inch  in  diameter  is  held  twelve  inches  from  a  lens 
which  has  a  principal  focus  of  four  inches.  Where  will  the  image 
be  formed  and  what  will  be  its  size?    Show  the  calculation. 

Parallel  rays  of  light  passing  through  this  lens  would  be 
brought  to  focus  at  a  distance  of  four  inches.  If  the  coin  was 
placed  at  twelve  inches  the  rays  would  be  divergent  and  would 
reduce  the  power  of  the  lens  and  throw  the  focus  farther  away. 
As  these  inch  numbers  must  be  expressed  in  fractions,  the  problem 
would  be  worked  out  by  the  usual  formula,  which  in  this  case 
would  be  >i  —1/12  =  1/6.  So  that  the  point  where  the  image 
would  be  six  inches  from  the  lens  and  on  the  opposite  side  from 
the  object. 

Since  the  object  is  at  a  distance  of  twelve  inches  from  the 
lens  and  the  image  at  a  distance  of  six  inches  from  it,  which  is 
just  one-half  the  distance,  the  size  would  be  one-half  the  size 
of  the  object,  or  one-half  inch. 


Transpose  into  their  plus  and  plus  equivalents: 

a  +  1.50  D.  sph.  C  -  .37  D.  cyl.  X  10° 
b  -f  5.00  D.  sph.  C  -  4.50  D.  cyl.  X  150° 
c  +  4.25  D.  sph.  C   -  1.75  D.  cyl.  X    35° 

The  rules  that  guide  us  are  as  follows: 

The  sphere  is  obtained  by  the  algebraic  addition  of  the  sphere 
and  cylinder. 

The  cylinder  remains   the  same,   but  its  sign  and   axis  is 
changed. 

Using  these  rules  the  results  will  be 

a  +  1.13  D.  sph.  C  +  .37  D.  cyl.  axis  100° 
b  +  .50  D.  sph.  C  -f  4.50  D.  cyl.  axis  60° 
c  +  2.50  D.  sph.  C  +  1.75  D.  cyl.  axis  125° 


10 


Stale  Board  Examinations 


Transpose  into  sph.  cyl.  form: 

a  -f  2.25  D.  cyl.  X  10°  :2  -{-  2.25  D.  cyl.  X  100° 
b  -  1.75  D.  cyl.  X  70°  C:  -\-  3.00  D.  cyl.  X  160° 
c  +    .75  D.  cyl.  X  55°  O  -  1.75  D.  cyl.  X  145° 

a.  As  this  shows  the  same  power  in  both  meridians,  and  as 
these  meridians  are  at  right  angles,  the  transposition  would 
result  not  in  a  sphere-cylinder,  but  in  a  simple  sphere  of  the  same 
power.    The  answer  is  +  2.25  D.  sphere. 

b.  The  rules  for  the  transposition  of  cross-cylinders  are  as 
follows : 

1.  Take  either  one  of  the  cylinders  for  the  sphere. 

2.  Take  the  algebraic  difference  for  the  cylinder,  retaining 
the  sign  and  axis  of  the  cylinder  that  was  not  taken  for  the 
sphere. 

Illustrate  by  three  simple  diagrams  the  law  of  reflection  for  a 
luminous  point  centrally  placed  before  a  plane,  a  convex  and  a 
concave  mirror  respectively. 


Fig.  1 


The  law  of  reflection  is  that  the  angle  of  reflection  is  the  same 
as  the  angle  of  incidence.    This  law  is  illustrated  in  the  preceding 


Theoretic  Optics  11 

diagram  of  a  plane  mirror  where  A  B  [s  the  incident  ray  proceed- 
ing from  the  candle  and  B  C  the  reflected  ray. 

The  law  of  reflection  is  again  illustrated  in  the  second 
diagram,  Fig.  2,  representing  a  concave  mirror  where  the  parallel 
rays  proceeding  from  A  and  B  and  striking  C  and  D  are  reflected 
according  to  the  law  and  meet  at  F. 


Fig.  2 


The  law  of  reflection  is  also  illustrated  in  the  third  diagram, 
Fig.  3,  representing  a  convex  mirror,  where  the  parallel  rays 
proceeding  from  A  and  B  and  striking  C  and  D  are  reflected 
according  to  the  law  and  diverge  as  if  coming  from  F. 


Give  the  formula  that  defines  the  conjugate  focal  distances  u 
and  vfor  a  spheric  mirror,  expressed  in  terms  of  the  object  distance  u, 
the  image  distance  v  and  the  radius  r. 

The  refractive  power  of  a  lens  is  inversely  proportional  to 
its  focal  length.  For  example  if  F  represents  the  focal  length 
1/  F  would  represent  the  refractive  power  of  a  lens. 

If  M  represents  the  distance  of  the  object 

U  V  represents  the  distance  of  the  image 

If/  represents  the  distance  of  the  principal  focus 

If  r  represents  the  radius  of  curvature, 

then  we  have  the  formula 

1,112 
=  ^  or  — 

u         V        f         r 

If  index  is  approximately  1.50,  the  focal  length  will  be  twice 


12 


State  Board  Examinations 


the  radius  of  curvature  (2  r)  for  piano  lenses,  while  in  biconvex 
lenses  the  focal  length  is  equal  to  the  radius  (F  =  r). 


F<^ 


Fig.  3 

When  all  of  the  distances,  ii  of  the  object,  v  of  the  image  and 
the  radius  of  curvature  r  from  the  pole  on  the  axis  of  a  spheric 
mirror  are  counted  positive  in  the  direction  opposite  to  light  incidence, 
is  the  mirror  convex  or  concave  and  is  the  image  real  or  virtual? 

In  this  diagram,  Fig  4,  the  rays  proceed  from  B,  which  is 
situated  beyond  the  center  of  curvature  C,  and  are  focussed  at  D. 


Fig.  4 

These  conditions  correspond  to  those  mentioned  in  the 
question  and  the  mirror  is  concave  and  the  image  is  real. 

Give  the  value  of  the  principal  focal  distance  f  of  a  spheric 
mirror,  as  deduced  from  the  general  formula  for  conjugate  focal 
distances. 

The  formula  is  1  1     _    1 

"[i   +  ^    ~  T 

If  the  distance  of  the  object  is  30  inches  and  the  distance 
of  the  image  is  10  inches,  then  the  principal  focus  is  lyi,  which 
we  get  by  substituting  values  as  follows: 

1 

7K 


1+  1 
30  ^   10 


Theoretic  Optics 


13 


Construct  a  diagram  in  which  the  linear  dimensions  of  the 
object  0  and  the  image  i  are  represented  by  lines  perpendicular  to 
the  axis  at  a  greater  distance  than  the  focus  of  a  concave  mirror  and 
deduct  therefrom  the  ratio  of  magnification  expressed  in  terms  of 
the  focus  f  and  the  distance  ii  of  the  object. 

In  this  diagram,  Fig.  5,  ^1  F  £  is  a  concave  mirror,  F  X  is 
the  principal  axis  which  passes  through  the  center  of  curvature 
C  and  the  principal  focus  F.  B  D  is  a  luminous  object  in  front 
of  the  mirror  at  a  distance  D  V  from  the  mirror. 


Fig.  5 


One  of  the  rays  of  light  from  the  point  B  will  pass  through 
the  center  of  curvature  C  and  will  strike  the  mirror  at  the  point 
E.  As  it  is  incident  in  the  same  direction  as  a  radius  of  curvature 
it  is  perpendicular  to  the  arc  of  the  circle  and  hence  will  be 
reflected  back  along  the  same  line  as  it  came. 

Another  ray  of  light  from  the  point  B,  running  parallel  to 
the  axis  strikes  the  mirror  at  A  and  is  reflected  at  such  an  angle 
as  to  pass  through  the  principal  focus  F. 

In  its  further  progress  it  intersects  the  first-mentioned  ray 
at  B' ,  which  is,  therefore,  the  image  point  of  B.  Consequently, 
D'  B'  is  a  real  and  inverted  image  oi  B  D  and  it  is  apparent  from 
the  diagram  that  the  image  is  smaller  than  the  object. 

The  reverse  of  the  above  would  also  be  true.  Suppose 
D'  B'  was  the  object  a  parallel  ray  B'  H  after  reflection  would 
pass  through  F;  and  another  ray  from  B'  drawn  through  the 
center  of  curvature  C  would  be  reflected  back  upon  itself  and 
the  two  rays  would  intersect  at  B.  Consequently  B  D  would, 
be  the  magnified  image  of  D'  B' . 


14 


State  Board  Examinations 


If  i  represents  the  image  and  o  represents  the  object,  the 
magnification  or  minification  would  be  expressed  by  the  fraction 
i/o. 

The  triangles  B  D  F  and  V  H  F  are  similar  and  their  cor- 
responding sides  are  proportional. 

D'  V  is  distance  of  object  from  mirror  =  u.  F  V  is  distance 
of  focus  from  mirror  =  /. 

D'  B'  =  object  =  0 

B  D  =  image  =  i 
therefore 

I       B  D 


Also 


0      D'  B' 

D  F,      u  -f 
or 


F  V 


f 


What  is  meant  by  the  index  of  refraction? 

The  index  of  refraction  is  the  numerical  expression  which 
indicates  the  refractivity  of  a  medium  as  compared  with  air, 


Fig.  6 

which  is  taken  as  the  standard  or  unit  or  1,  and  hence  every  other 
medium  being  denser  has  an  index  greater  than  1.  The  index 
of  refraction  depends  upon  the  relation  or  ratio  which  constantly 
exists  between  the  sine  of  the  angle  of  incidence  and  the  sine  of 
the  angle  of  refraction. 


Theoretic  Optics 


15 


In  order  to  illustrate  the  course  of  a  ray  of  light  as  it  passes 
from  one  medium  to  another  of  different  density,  Fig.  6,  let  G  H 
represent  a  refracting  surface  separating  air  with  an  index  of  1.00 
from  glass  with  an  index  of  1.50.  Let  J  K  be  a  ray  incident  on 
the  surface  of  the  point  K,  to  which  the  line  L  K  M  is  the  normal 
or  perpendicular;  then  J  K  Lis  the  angle  of  incidence  and  P  K  M 
is  the  angle  of  refraction. 

If  we  represent  the  angle  of  incidence  by  the  letter  i  and  the 
angle  of  refraction  by  the  letter  r,  then  the  formula  for  ascertain- 
ing the  index  of  refraction  of  any  substance  is  expressed  as 
follows : 

sin  i    _   L  J 

sin  r        P  M 

\i  L  J  equals  3  and  P  M  equals  2,  then  the  first  divided  by 
the  second  equals  1.50  representing  the  index  of  refraction  of 
the  glass  as  compared  with  the  standard  taken  or  air. 


Give  the  general  formula  that  defines  the  conjugate  focal  distayice 
u  and  V  and  for  a  convex  refracting  surface  tvhose  radius  is  r  and 
whose  refractive  index  is  n,  the  object  being  at  a  distance  u  and  the 
image  at  a  distance  v  from  the  pole;  also  state  in  which  direction 
from  the  pole  the  distances  on  the  principal  axis  are  counted  positive 
or  negative  with  respect  to  the  direction  of  incidence. 


Fig.  7 


In  this  figure,  Fig.  7,  the  rays  proceeding  from  the  object  0 
are  converged  after  refraction  and  form  the  image  /.  Each  is  a 
real  focus  and  the  two  are  called  conjugate  foci.  The  convexity 
of  the  surface  is  turned  toward  the  incident  wave. 

r    =  radius. 

n  =  refractive  index  rarer  medium. 

n'  =  refractive  index  of  denser  medium. 


16  State  Board  Examinations 

u  =  distance  of  object. 

V   =  distance  of  image. 

n 


+ 


AC)   '    A  I  r 

Substituting  u  for  0  A  and  F  for  ^  /  respectively  we  have 


n        n  _  n    —  n 
u        V  r 


This  equation  expresses  the  relation  between  the  conjugate 
focal  distance,  A  0  and  A  I.  U\s,  positive  when  measured  in  a 
direction  opposite  to  the  incident  light  and  negative  when  meas- 
ured in  the  other  direction. 


Fig.  8.     (See  opposite) 

In  the  above  formula  which  value  must  be  given  to  u  so  as  to 
obtain  the  second  principal  focal  distance  v,  commonly  designated 
as  fi? 

If  0  is  situated  at  such  a  distance  that  its  rays  are  parallel, 
the  distance  A  0  or  u  must  be  regarded  as  infinity  and  then  n/u 
must  equal  zero. 

Making  this  substitution  in  the  foregoing  equation  we  have 

n'   _   n'   —  n 
V  r 

from  which  we  derive  the  corresponding  value  of  v  or  f^. 

u'  r 


V  = 


n    —  n. 


What  is  the  direction  of  the  refracted  ray  with  respect  to  the 
second  principal  focus  when  the  incident  ray  is  parallel  to  the  axis 
of  a  spheric  refracting  surface? 


Theoretic  Optics  17 

From  the  formula  given  in  the  previous  answer  we  ascertain 
the  focusing  point  for  rays  that  are  parallel  before  refraction. 
The  distance  of  this  point  from  the  surface  is  the  posterior  or 
second  principal  focal  distance  and  is  often  denoted  by  the  letter 
fi,  the  value  of  which  is  derived  from  the  equation  just  mentioned. 


SJiow  in  a  simple  diagram,  by  means  of  the  principal  lines  of 
direction,  the  positions  of  the  first  and  second  principal  foci,  Fi 
and  F2,  with  respect  to  a  luminous  point  slightly  above  the  principal 
axis,  nearer  than  the  focus  and  located  to  the  right  and  in  front  of 
a  concave  refracting  surface. 

Let  A  represent  a  luminous  point,  from  which  a  parallel 
ray  of  light  after  refraction  by  the  concave  surface  will  diverge 
as  if  proceeding  from  the  point  f^  which  is  the  second  principal 
focal  distance.  A  divergent  ray  from  A  striking  the  concave 
refracting  surface  at  B  will  after  refraction  be  parallel  to  the  axis 
and  appear  to  proceed  from  the  point  Fj.    (Figure  8,  opposite.) 


From    the    general   formula    for    conjugate   focal    distances, 

for  a  thin  lens  having  a  radius  of  curvature  rx  for  the  first  surface, 
{exposed  to  incidence)  and  a  radius  ro  for  the  second  surface,  give 
the  value  of  the  second  principal  focal  distance  fi. 

If  u  equals  infinity,  then 


—ox-^=  {n  -  1)1 I 


It  being  true  that  the  first  and  second  principal  focal  distances 
f\  and  fi  for  a  thin  lens  are  equal,  give  the  equation  from  which  the 
focal  length  f  may  be  deducted. 

If/  be  the  focal  length  of  a  thin  convex  lens,  then 


^=<"-'>(^^.) 


18  State  Board  Examinations 

Or  if  each  surface  has  the  same  radius  of  curvature  the  formula 
may  be  written 


What  are  the  laws  of  refraction? 

A  ray  of  Hght  striking  a  medium  perpendicularly  is  not  bent. 

A  ray  of  light  striking  a  medium  obliquely  in  passing  from 
a  rare  to  a  denser  medium  is  bent  toward  the  perpendicular. 

A  ray  of  light  striking  a  medium  obliquely  in  passing  from 
a  dense  to  a  rarer  medium  is  bent  from  the  perpendicular. 


Define  principal  focus,  ordinary  focus  and  conjugate  foci. 

The  principal  focus  is  the  focal  point  for  parallel  rays. 

An  ordinary  focus  is  the  meeting  point  for  rays  which  di- 
verge from  some  point  inside  of  infinity  and  are  brought  together 
at  some  point  beyond  the  principal  focus. 

Conjugate  foci  are  interchangeable,  so  that  the  rays  which 
diverge  from  one  will  always  converge  to  the  other. 


What  two  factors  determine  the  dioptric  power  of  a  lens? 
Index  of  refraction  and  radius  of  curvature. 


When  light  passes  from  a  medium  which  is  optically  dense  to 
one  that  is  optically  rare,  what  change  in  the  direction  of  the  light 
is  there? 

If  the  ray  of  light  strikes  the  medium  perpendicularly,  it 
passes  unchanged;  if  it  strikes  it  obliquely  it  is  bent  away  from 
the  perpendicular. 

What  is  the  rule  for  figuring  the  radius  of  curvature  of  lenses, 
the  index  of  refraction  being  given,  and  the  focal  power  of  the  lens? 

The  radius  of  curvature  divided  by  the  index  of  refraction 
less  unity,  equals  the  focus  of  a  plano-convex  lens.  Hence  the 
index  of  refraction,  less  unity,  multiplied  by  the  focal  power  of 
the  lens,  equals  the  radius  of  curvature. 


Theoretic  Optics  19 

Suppose  the  index  of  refraction  is  1.50  and  the  focal  length 
of  the  lens  20  cm.,  then  we  have 

(1.50  —  1)  X  20  =  10  cm.,  which  is  the  radius  of  curvature. 


The  focal  length  of  a  convex  lens  is  12  cm.;  an  object  is  placed 
20  cm.  in  front  of  the  lens.  Where  will  the  image  he  and  will  it  he 
erect  or  inverted?    Show  the  process  of  the  figuring. 

If  the  focal  length  of  the  convex  lens  is  12  cm.,  the  refractive 
power  of  the  lens  is  8.33  D.  The  focal  length  of  curve  refers  to 
parallel  rays  before  entering  the  lens.  If  such  rays  are  divergent 
the  focus  is  thrown  farther  away,  according  to  the  degree  of 
divergence. 

If  the  rays  proceed  from  a  distance  of  20  cm.  they  would 
have  a  divergence  of  5  D.,  which  must  be  subtracted  from  8.33  D., 
leaving  3.33  D.,  which  means  a  focal  distance  of  12  inches  or 
30  cm. 

Or  using  the  reciprocals  we  have  the  following  equation : 

J__  J_  ^J_ 

12      20      30 


Having  a  hiconcave  lens,  it  is  found  that  using  one  surface 
as  a  mirror  the  image  of  a  distant  ohject  is  at  8  inches  from  the 
surface;  while  testing  the  other  surface  in  the  same  way,  the  focus 
is  4  inches.  What  will  he  the  power  of  the  lens  if  the  refractive 
index  of  the  glass  is  1.50? 

Inasmuch  as  the  principal  focus  of  a  mirror  is  one-half  the 
radius,  therefore  an  8-inch  focus  would  indicate  a  16-inch  radius, 
or  a  2.50  D.  value;  and  a  4-inch  focus  an  8-inch  radius  or  5  D. 
value. 

Now  the  formula  for  focal  distance  is  as  follows: 

or  substituting  values: 

-^=U.50-7)(-j+-^) 


20  State  Board  Examinations 


or 

/ 


or 


=  (.50)  {-  5D.  ->r  -  2.50  D.) 
r 


4  =   -  3.75  D. 
F 


At  what  distance  will  parallel  rays  be  focused  by  a  concave 
mirror  whose  radius  of  curvature  is  17  inches? 

The  principal  focus  of  a  concave  mirror  is  always  equal  to 
half  the  radius  of  curvature;  therefore,  in  this  case,  parallel  rays 
will  be  focused  at  S}4  inches. 


What  is  the  radius  of  curvature  of  a  plus  1.50  lens,  crown  glass? 

The  index  of  refraction  is  not  mentioned;  it  may  vary  from 
1.48  to  1.56  or  even  1.60,  but  for  sake  of  illustration  we  will 
say  it  is  1.50. 

Then  we  have  focus  multiplied  by  index  less  unity  equals 
radius  of  curvature,  or  substituting  figures 
26  X  (1.50  -  1)  =  13 

Therefore,  13  inches  is  the  radius  of  curvature  if  the  lens  is 
piano,  as  proved  by  the  rule  that  the  focal  length  of  a  plano- 
convex lens  is  equal  to  t'A\ace  the  length  of  its  radius. 

'If  the  lens  is  biconvex  we  have 

26  X  2  (1.50  -  1)  =  26 

Here  26  inches  is  the  radius  of  curvature  as  proving  the  rule 
that  the  focal  length  of  a  biconvex  lens  is  equal  to  its  radius. 


What  radius  of  curvature  must  be  ground  on  the  two  surfaces 
of  a  periscopic  lens,  one  of  the  surfaces  to  be  on  a  radius  of  5  cm., 
the  total  dioptric  power  to  be  8  D.,  and  the  refractive  index  to  be 
1.50?    How  is  it  ivorked  out?    In  inches  or  millimeters? 

If  the  radius  of  curvature  of  one  surface  is  5  cm.  then  accord- 
ing to  the  rule  that  the  focal  length  is  twice  the  radius,  the  focal 
length  of  this  surface  is  10  cm.  which  means  that  the  value  of 
this  surface  is  +  10  D. 


Theoretic  Optics  21 

Now  then,  if  the  total  power  of  the  lens  is  +  8  D.,  the 
opposite  must  show  a  —  2  D.  curve,  or  20  inches.  If  according 
to  the  rule  this  is  twice  the  length  of  the  radius,  the  latter  must 
be  10  inches. 

If  the  index  had  been  other  than  1.50  the  results  would  have 
been  slightly  different. 

//  a  point  of  light  is  at  a  distance  of  16  inches  from  a  +  4.50 
D.  lens,  where  will  the  light  he  fociissed? 

The  rays  diverging  from  a  point  of  light  at  a  distance  of 
16  inches  will  require  +  2.50  power  to  overcome  this  divergence 
and  make  them  parallel.  This  leaves  +  2  power  of  the  +  4.50  D. 
lens  to  act  on  these  parallel  rays,  which  will  be  brought  to  a 
focus  at  20  inches. 

A  2  D.  lens  decentered  5  mm.  will  produce  how  much  prismatic 
action? 

According  to  the  standard  there  is  1°  prismatic  power 
developed  for  every  1  D.  of  refractive  power  wnth  a  decentration 
of  10  mm.,  and  >^°  for  every  1  D.  lens  with  a  decentration  of 
5  mm. 

The  question  asks  how  much  prismatic  action.  We  do  not 
know  whether  the  framer  of  the  question  had  in  mind  prismatic 
power  or  deviation,  but  to  cover  both  phases  the  answer  would 
be  as  follows:  1°  of  prismatic  power  and  as  the  angle  of  deviation 
is  one-half  the  principal  angle,  yi°  of  deviation. 


Object  is  10  inches  high  and  its  distance  from  the  mirror  is 
40  inches;  the  image  formed  by  the  mirror  is  5  inches  distant;  what 
is  the  height  of  the  image? 

The  height  of  the  image  bears  the  same  relation  to  the 
height  of  the  object  as  the  distance  of  the  image  bears  to  the 
distance  of  the  object. 

Let  X  represent  height  of  image  which  it  is  desired  to  find 
and  using  the  known  values  we  have 

X  :  10  ::  5  :  40 
10  X  5       50       .,. 


22  State  Board  Examinations 

Object  is  80  inches  from  a  mirror;  its  image  is  20  inches  from 
mirror  and  is  2  inches  high.    Ho-n'  high  is  the  object? 

The  same  proportion  holds  good  as  in  previous  question. 
Using  X  for  the  unkncnvn  quantity  and  substituting  the  values 
as  gi\'en  we  have 

20  :  80  : :  2  :  x 
Then 

^  80  X  2  ^   160  ^  8 
■^"  20       ~    20   ~   1 

Or  X  =  8  inches,  which  is  the  height  of  the  object. 


The  object  is  24  inches  n'ide  and  its  image  is  3  inches  wide. 
The  distance  of  the  object  from  the  mirror  is  32  inches;  what  is  the 
distance  of  the  image? 

The  width  of  the  object  bears  the  same  relation  to  the  width 
of  the  image  as  the  distance  of  the  object  bears  the  distance  of 
the  image. 

The  first  three  values  are  given  and  the  fourth  or  the  un- 
known will  be  represented  by  x.  and  then  we  have  the  following 
proportion: 

24  :   3  ::   32  :  X 

Then 

_  32  X  3  ^  96  _  4 
^  ~        24       ~  "24  ~  1" 

Or  X  =  4  inches,  which  will  be  the  distance  of  the  image. 


Let  the  image  be  2  inches  high  and  the  object  20  inches  high; 
let  the  distance  of  the  image  be  4  ijiches;  what  will  be  the  distance 
of  the  object  from  the  mirror? 

The  size  of  the  image  is  to  the  distance  of  the  image  as  the 
size  of  the  object  is  to  the  distance  of  the  object,  which  may  be 
expressed  as  follows: 

2  in.  :  4  in.  ::  20  :  x 

Then 

■^  X20      80 
X  = =  -—-=  40  inches 

which  is  the  distance  of  the  object. 


Theoretic  Optics  23 

In  the  preceding  example  ivhat  will  be  the  power  of  the  mirror 
if  it  is  convex? 

The  general  formula  for  mirrors  is  as  follows: 

u   ^    V  F 

It  must  be  borne  in  mind  that  the  formula  for  a  convex 
mirror  is  the  same  as  that  for  a  concave  mirror,  but  in  working 
with  these  formulae  it  is  necessary  to  remember  that  in  the 
case  of  the  convex  mirror  v  is  always  a  negative  quantity,  because 
the  focus  of  a  convex  mirror  is  not  real  but  virtual. 

Hence  the  formula  would  be 

u  V  r 

or  substituting  the  values  given  in  the  previous  question, 

1  D.  +  -  10  D.  =   -  9  D. 
which  is  the  negative  focus  or  power  of  the  convex  mirror. 


Solve  the  same  problem  by  the  formula,  but  the  mirror  to  be 
concave. 

Here  the  quantities  are  all  positive,  and  using  the  values 
given  in  the  previous  question  expressed  in  diopters,  we  have 

1  D.  +  10  D.  =   +  11  D. 
as  the  positive  focus  or  power  of  the  concave  mirror. 


A  ray  of  light  is  incident  on  a  plaiie  surface  at  an  angle  of  60° 
with  the  normal;  the  refracted  ray  forms  an  angle  with  the  normal 
of  45°.  The  sine  of  45°  is  0.707,  and  the  sine  of  the  angle  60°  is 
0.866;  how  is  the  index  of  refraction  found  and  what  is  it  in  this 
particular  case? 

To  find  the  index  of  refraction  of  any  substance  as  compared 
with  air,  it  is  necessary  to  divide  the  sine  of  the  angle  of  incidence 
by  the  sine  of  the  angle  of  refraction.  In  this  case  we  divide  the 
sine  of  the  angle  of  incidence  (0.866)  by  the  sine  of  the  angle  of 
refraction  (0.707)  and  the  result  of  1.225  approximately  as  the 
index  of  refraction  in  this  case. 


24  State  Board  Examinalions 

What  is  the  relation  of  size  of  image  to  object  as  compared 
with  the  distance  of  these  from  a  lens,  and  is  there  any  difference  in 
the  rule  icith  a  convex  and  a  concave  lens^ 

The  size  of  the  image  is  to  the  size  of  the  object,  as  the  dis- 
tance of  the  image  is  to  the  distance  of  the  object.  This  applies 
to  both  convex  and  concave  lenses,  and  when  any  three  of  these 
values  are  known  the  fourth  can  be  figured  out. 


What  effect  has  obliquity  on  the  image  of  a  point  of  light,  such 
as  an  ilhimined  pinhole  in  a  sheet  of  black  paper  when  formed  by 
a  thin  convex  lens? 

The  production  of  a  more  or  less  irregular  blur  in  place  of 
a  true  point  image.  There  is  an  increase  in  the  refractive  power 
of  all  meridians  of  the  lens,  but  especially  so  in  the  meridian  at 
right  angles  to  the  axis  of  rotation,  thus  developing  the  effect 
of  a  stronger  sphere  with  the  addition  of  a  cylindrical  element. 


The  focus  of  a  concave  mirror  is  20  inches;  where  will  be  the 
image  of  an  object  placed  at  the  folloiving  distances  from  the  mirror: 
20  inches,  40  inches,  infinity? 

If  an  object  be  placed  at  20  inches  from  a  20-inch  concave 
mirror;  in  other  words  if  the  object  be  placed  at  the  focal  distance 
of  a  concave  mirror  its  image  will  be  at  infinity. 

If  the  object  be  placed  at  40  inches  the  mirror  must  first 
overcome  the  divergence  of  rays  proceeding  from  this  distance, 
leaving  a  sufificient  convergence  to  bring  the  rays  to  a  focus  at 
40  inches. 

If  the  object  was  placed  at  infinity  the  image  would  be 
formed  at  the  focal  distance  of  the  lens,  which  is  20  inches. 


Where  must  an  object  be  placed  to  obtain  a  real  image  four 
times  the  size  of  the  object,  using  a  -f  2.50  D.  lens? 

If  image  and  object  are  at  the  same  distance  from  the  lens 
they  will  be  of  the  same  size  and  the  image  will  increase  in  size 


Theoretic  Optics  25 

in  proportion  to  its  distance.  Therefore  in  order  to  obtain  a 
real  image  four  times  the  size  of  the  object  its  distance  must  be 
increased  four  times. 

In  this  case  the  lens  is  a  +  2.50  D.  with  a  focal  distance  of 
16  inches  of  which  one-fifth  will  represent  distance  of  image  and 
four-fifths  distance  of  the  object.  This  is  1  80  and  1  20  re- 
spectively, or  80  inches  for  the  distance  of  the  image  and  20  inches 
for  distance  of  object.  This  is  proven  to  be  correct  by  the 
transposition  of  these  inch  numbers  into  diopters  80  inches  =  .50 
D.  and  20  inches  =  2  D.,  the  sum  of  which  is  2.50  D.,  the  number 
of  the  lens  given  in  the  question. 


How  is  the  curvature  of  a  spherical  wave  oj  light  measured? 
How  would  you  verify  the  fact  that  when  a  spherical  wave  of  light 
passes  directly  through  a  thin  lens  the  change  in  the  curvature  of 
the  wave  is  the  same  for  all  positions  of  the  lens? 

The  curvature  of  the  wave  front  is  inversely  proportional  to 
the  distance  of  its  source,  and  hence  the  curvature  of  a  spherical 
wave  of  light  is  measured  by  the  reciprocal  of  that  distance. 
If  a  one  meter  length  of  radius  be  taken  as  the  unit,  the  curvature 
of  the  wave  front  at  a  distance  of  one  meter  is  said  to  be  1  D. 
At  half  a  meter  it  is  2  D.,  at  one-third  meter  3  D.,  and  at  two 
meters  .50  D. 

Parallel  rays  of  light  or  a  plane  wave,  passing  through  a 
1  D.  lens,  will  be  given  a  curvature  of  1  D.,  and  so  on. 

In  order  to  prove  that  the  change  in  curvature  of  a  spherical 
wave  in  passing  through  a  thin  lens  is  constant,  we  fall  back 
upon  the  regular  formula  for  conjugate  foci: 

in  which  o  represents  the  distance  of  the  object,  i  the  distance  of 
the  image  and  /  the  principal  focus. 

—  expresses  the  curvature  of  the  wave  diverging  from  the 
object  and  meeting  the  lens,  —■  the  curvature  of  those  leaving  the 

lens  to  form  the  image  and  -j  the  focal  length  of  the  lens.      The 

.    1  .    .  1 

latter  must  be  a  constant  and  if  ^  is  increased  or  diminished,  -j 

must  be  decreased  or  increased  in  the  same  ratio. 


26  State  Board  Examinations 

If  the  curve  of  a  biconvex  lens  on  one  surface  is  on  a  radius  of 
13^2  inches  a7id  on  the  other  on  a  40-inch  radius,  what  is  the  power 
of  the  lens? 

Such  a  lens  is  equivalent  to  one  plano-convex  lens  with  a 
radius  of  3  D.  and  another  plano-convex  lens  of  1  D.  radius. 
Now,  then,  the  focal  length  of  a  plano-convex  lens  is  equal  to 
twice  the  length  of  its  radius,  or  what  is  equivalent  to  the  same 
thing  one-half  its  refracti\e  power.  Applying  this  rule  we  find 
the  combined  power  of  the  two  surfaces  is  4  D.,  one-half  of 
which  is  2  D.,  and  this  represents  the  power  of  the  lens. 


In  what  three  ways  may  light  he  affected? 

It  may  be  refracted,  reflected  or  absorbed.     Or  its  velocity 
may  be  increased  or  diminished,  or  bent  out  of  its  course. 


What  is  an  image  and  how  is  it  formed? 

An  image  is  the  exact  reproduction  of  an  object,  and  is 
formed  by  refraction  through  a  lens  or  reflection  from  a  mirror. 

There  are  two  kinds  of  images,  real  and  virtual.  The  first 
is  formed  by  a  meeting  of  the  rays,  it  has  an  actual  existence  and 
may  be  projected  upon  a  screen.  The  second  is  only  an  imag- 
inary image  such  as  would  be  formed  by  a  prolongation  back- 
ward of  the  diverging  rays  of  light. 


What  is  a  ray  of  light  called  before  passing  from  one  medium 
to  another? 

An  incident  ray. 


What  is  a  ray  of  light  called  after  it  has  passed  from  one 
medium  into  another? 

A  refracted  ray. 


What  is  spherical  aberration? 

Spherical  aberration  is  the  wandering  of  rays  from  a  single 


Theorelic  Optics  27 

focus,  or  the  focusing  of  the  rays  of  Hght  passing  through  a  lens 
at  varying  distances  from  the  lens,  the  rays  passing  through 
the  periphery  coming  to  a  sooner  focus  than  the  more  central 
rays.  This  is  due  to  the  fact  that  the  curvature  and  therefore 
the  refractive  power  of  the  lens  increases  from  the  center  (where 
it  is  nothing)  to  the  periphery  (where  it  is  greatest). 


What  is  chromatic  aberration? 

Chromatic  aberration  is  due  to  dispersion  of  light  on  account 
of  the  difference  in  refraction  of  the  different  colors  of  which 
white  light  is  composed.  As  a  result  in  the  image  formed  by  an 
ordinary  lens,  the  outlines  of  the  figures  will  be  found  to  be 
edged  with  rainbow  hues.  The  seven  primary  colors  each  have 
a  different  degree  of  refrangibility,  the  red  being  least  refracted, 
the  violet  most,  the  other  colors  in  regular  order  between  these 
extremes. 

//  light  is  reflected  away  from  the  normal  or  perpendicular, 
what  is  the  cause?     If  toward  the  perpendicular? 

In  the  first  case  on  "account  of  the  passage  of  rays  from  a 
dense  to  a  rare  medium;  and  in  the  second  case  the  passage  of 
li^^ht  from  a  rare  to  a  dense  medium. 


What  is  a  virtual  focus? 

This  is  synonymous  with  a  negative  focus,  and  is  the  point 
from  which  rays  appear  to  diverge  after  passing  through  a 
concave  lens,  or  after  reflection  from  a  convex  mirror,  or  after 
refraction  by  convex  lens  when  object  is  closer  than  its  principal 
focal  distance,  or  after  reflection  from  a  concave  mirror  when 
object  is  closer  than  its  principal  focal  distance. 


What  is  reflection  of  light? 

This  is  the  throwing  back  of  rays  of  light  from  the  surface 
on  which  they  fall  into  the  same  medium  through  which  they 
came.  The  best  form  of  a  reflector  is  a  mirror  or  a  polished  metal 
surface.     But  even  if  the  body  is  transparent  and  the  rays  are 


28  State  Board  Exaniinations 

transmitted,  yet  some  (jf  them  are  reflected  and  it  is  by  these 
reflected  rays  that  objects  are  made  visible. 


What  is  refraction  of  light? 

The  deviation  which  takes  place  in  the  direction  of  a  ray 
of  light  as  it  passes  from  one  medium  into  another  of  different 
density.    The  two  laws  that  govern  refraction  are: 

1.  In  passing  from  rare  to  dense  medium,  bent  toward  the 
perpendicular. 

2.  In  passing  from  dense  to  rare  medium,  bent  from  the 
perpendicular. 

Where  is  the  principal  focus  of  a  lens? 

At  the  principal  focal  distance  of  a  lens,  that  is  where 
parallel  rays  are  made  to  meet  after  being  refracted  by  a  convex 
lens.  If  the  rays  that  enter  the  lens  are  convergent  or  divergent 
instead  of  parallel,  the  focus  would  be  shortened  or  lengthened, 
but  it  would  not  be  the  principal  focus. 


What  are  conjugate  foci? 

The  point  from  which  rays  originate  and  diverge  and  the 
point  on  the  other  side  of  the  lens  on  the  axial  ray  where  they 
come  together  are  conjugate  to  each  other,  and  are  known  as 
conjugate  foci.  Either  one  may  be  considered  as  the  object  and 
the  other  will  be  the  image. 


What  is  the  difference  in  the  image  as  formed  by  a  concave 
spherical  mirror  and  a  convex  spherical  mirror? 

Assuming  the  object  to  be  at  a  distance  so  that  the  rays  that 
strike  the  mirror  are  parallel,  the  image  formed  by  a  concave 
mirror  is  real,  inverted,  and  in  front  of  the  mirror  and  can  be 
caught  upon  a  screen;  while  that  formed  by  a  convex  mirror  will 
be  virtual,  erect,  behind  the  mirror  and  cannot  be  caught  upon 
a  screen. 


Theoretic  Optics  29 

What  is  the  conjugate  focus  to  a  point  ivkich  is  2  inches  from 
a  minus  lens  -with  a  principal  focus  of  3  inches? 

If  the  source  of  light  is  at  a  distance  of  2  inches  the  rays  of 
Hght  would  have  a  divergence  equal  to  —  20  D.,  which  will  be 
increased  to  33  D.  by  passing  through  a  concave  lens  with  a 
divergence  of  13  D.,  as  shown  by  the  principal  focus  of  3  inches. 
This  33  D.  will  show  a  virtual  focus  at  about  1  1/5  inches  on  the 
same  side  of  the  lens  as  the  object  is  situated;  and  therefore 
1  15  inches  would  be  conjugate  to  2  inches  in  this  case. 


A  plus  lens  has  a  principal  focus  of  40  cm.  and  the  radius 
of  curvature  of  one  of  its  surfaces  is  40  cm.;  what  is  the  radius 
of  curvature  of  the  other  surface,  the  index  of  refraction  of  the  glass 
being  1.5? 

In  a  biconvex  lens  the  focal  length  is  just  equal  to  its  radius; 
therefore  in  this  case,  where  the  principal  focus  is  identical  with 
the  radius  of  curvature  of  one  of  its  surfaces,  the  lens  must  be 
biconvex  and  the  radius  of  the  second  surface  the  same  as  that 
of  the  first,  viz.,  40  cm. 

//  the  index  of  refraction  of  a  certain  kind  of  glass  is  1.496 
on  zvhat  radius  of  curvature  must  a  plano-convex  lens  be  struck  so 
that  the  lens  will  be  a  1  D.  lens? 

The  rule  is,  focal  distance,  multiplied  by  index  of  refraction 
equals  radius  of  curvature  if  the  lens  is  piano.  Substituting 
figures,  we  have 

40  (1  D.)  X  (1.496  -  1) 

or  40  X  .496  =  19.84 

The  radius  of  curvature  would  have  to  be  19.84  inches. 


What  is  the  critical  angle  in  refraction  and  what  is  the  result 
of  same? 

This  is  the  least  angle  of  incidence  that  permits  a  ray  of 
light  traveling  in  a  dense  medium  to  pass  into  a  rare  medium, 
and  beyond  which  total  reflection  occurs  at  the  surface  which 
separates  the  two  media.  As  this  prevents  any  loss  of  light  from 
transmission  or  absorption,  the  reflection  will  be  the  most  brilliant 


30  Slate  Board  Examinations 

obtainable,   and   hence   this  method   is  made  use  of  in  optical 
instruments. 

The  critical  angle  from  water  to  air  is  48°  35',  which  means 
that  this  is  the  least  angle  that  will  permit  the  light  to  be  refracted 
and  pass  out  of  the  water.  If  the  rays  form  an  angle  greater  than 
48°  35',  they  will  not  pass  out  of  the  water  but  will  be  reflected 
back  into  it.  The  surface  separating  the  two  media  becomes  a 
reflecting  surface  and  acts  as  a  plane  mirror. 


What  is  the  conjugate  focus  to  a  point  36  centimeters  from  a 
biconvex  lens  of  2.5  D.? 

A  convex  lens  of  2.50  has  a  principal  focal  distance  of  40  cm., 
and  rays  proceeding  from  this  point  would  emerge  from  the  lens 
parallel.  If  they  proceed  from  a  point  farther  than  the  principal 
focus  they  will  emerge  from  the  lens  convergent  and  will  meet  at 
a  point  which  is  conjugate  to  that  from  which  it  proceeded.  On 
the  other  hand,  if  the  rays  proceed  from  a  point  closer  than  the 
principal  focus,  they  will  emerge  from  the  lens  as  divergent  and 
will  not  meet  in  a  focus. 

The  latter  is  the  condition  that  applies  in  this  question,  the 
principal  focus  being  at  40  cm.  and  the  rays  proceeding  from  a 
point  at  36  cm.  The  rays  will  emerge  still  divergent,  but  not  so 
much  so  as  before  entering  the  lens.  If  these  divergent  rays 
were  continued  backward  by  imaginary  lines  to  the  point  from 
which  they  appear  to  proceed,  that  point  would  be  conjugate  to 
the  first,  although  it  is  a  negative  focus  and  has  no  real  existence. 

The  question  is,  where  will  that  point  be  located  in  the  case 
under  consideration?  Rays  proceeding  from  36  cm.  will  have  a 
divergence  equal  to  2.85  D.  After  passing  through  the  +  2.5  D. 
lens  and  being  refracted  to  that  extent,  they  will  emerge  with  a 
divergence  equal  to  .35  D.,  which  represents  a  distance  of  114 
inches,  or  285  cm.  which  in  this  case  is  conjugate  to  the  36  cm. 


What  general  effect  do  plus  and  minus  lenses  have  on  diverging 
and  converging  light? 

Convex  lenses  act  on  diverging  rays  so  as  to  lessen  their 
divergence.  If  the  rays  proceed  from  some  distance  or  from  a 
point  beyond  the  principal  focus,  the  divergence  will  be  entirely 


Theoretic  Optics  31 

overcome  and  the  rays  made  convergent  and  brought  to  a  focus. 
If  proceeding  from  its  principal  focus,  the  convex  lens  would 
make  them  parallel.  If  proceeding  from  a  point  closer  than  the 
principal  focus,  the  convex  lens  would  reduce  their  divergence. 

The  convex  lenses  act  on  converging  rays  in  such  a  way  as 
to  make  them  more  convergent  and  bring  them  to  a  sooner  focus. 

Concave  lenses  act  on  divergent  rays  in  such  a  way  as  to 
increase  their  divergence. 

Concave  lenses  act  on  convergent  rays  to  lessen  their  con- 
vergence. If  their  divergence  corresponded  with  the  lens  they 
would  emerge  parallel;  otherwise  they  would  meet  in  front  of 
or  beyond  the  negative  focus  of  the  lens,  depending  upon  the 
degree  of  their  divergence. 

A  certain  lens  focuses  parallel  light  at  20  cm.;  what  lens 
must  he  placed  in  front  of  it  to  send  the  focus  hack  to  one  meter? 

The  lens  in  question  must  be  convex  and  if  it  focuses  parallel 
rays  at  20  cm.  this  must  be  its  principal  focal  distance,  in  which 
case  the  lens  would  be  +  5  D. 

In  order  to  throw  the  principal  focus  back  to  one  meter, 
the  strength  of  the  lens  must  be  reduced  to  +  1  D.  which  can  be 
accomplished  by  placing  in  front  of  the  original  lens  a  —  4  D. 


What  is  the  strength  of  a  lens  that  causes  light  coming  from  a 
point  133  cm.  away  to  pass  out  parallel? 

If  light  emerges  from  a  lens  in  parallel  lines  it  must  come 
from  a  point  at  the  principal  focus  of  the  lens,  because  the  latter 
is  conjugate  with  infinity,  as  represented  by  the  parallel  lines. 
Therefore  the  strength  of  the  lens  is  approximately  .75  D.,  which 
is  found  by  dividing  133  cm.  into  1  meter  (or  100  cm.). 


What  is  the  index  of  refraction  when  light  passes  from  water 
into  glass,  the  latter  having  a  refractive  index  of  1.546? 

The  law  of  refraction  is  expressed  by  the  following  formula: 
Sine  angle  incidence 


Sine  angle  refraction 


=  index  of  refraction. 


This  constant  quantity,  which  is  known  as  index  of  refrac- 
tion, represents  the  relative  velocity  of  light  in  the  two  media,  the 


32  State  Board  Examinations 

greater  the  density  the  less  the  velocity.  The  sine  of  the  angle 
of  incidence  always  bears  the  same  numerical  relation  to  the  sine 
of  the  angle  of  refraction,  no  matter  what  the  angle  of  incidence 
may  be. 

The  index  for  two  media  with  reference  to  each  other  is 
obtained  by  dividing  the  refractive  index  of  one  into  the  refrac- 
tive index  of  the  other. 

In  this  question  we  have  the  refractive  index  of  glass  given 
as  1.546,  which  we  divide  by  the  refractiv^e  index  of  water  (1.333), 

1.333)1.546(1.1597 
1.333 
2.130 
1.333 
7.970 
6665 


1.3050 

1.1997 

1.0530 

.9331 


A  certain  lens  in  air  has  a  power  of  6  diopters,  the  refractive 
index  of  the  glass  being  1.562;  what  will  he  the  dioptric  power  of 
this  lens  when  submerged  in  water? 

In  order  to  obtain  the  refractive  index  for  water  and  glass 
with  reference  to  each  other,  we  divide  the  index  of  glass  (1.562) 
by  the  index  of  water  (1.333),  and  the  result  is  1.171. 

In  order  therefore  to  compare  the  power  of  the  lens  in  water 
with  its  power  in  air,  we  must  make  use  of  the  proportion  of  the 
refractive  index  of  one  to  the  other. 

X  :  6  D  :  :  .171   :  .562 

.r  =  6D  x41^=  1-82  D. 
.562 

Therefore  the  power  of  this  6  D.  lens  when  submerged  in 
water  is  reduced  to  1.82  D. 


A  plus  8  D.  lens  made  of  glass  of  refractive  index  of  1.523  is 
cemented  inside  of  two  plates  ground  with  curves  to  match  its  surfaces, 
but  of  index  of  refraction  of  1.634;  what  is  the  power  of  the  lens 
in  its  new  position? 


Theoretic  Optics  33 

In  order  to  obtain  the  refractive  index  of  these  two  kinds 
of  glass  with  reference  to  each  other,  we  divide  the  index  of  one 
(1.523)  into  the  index  of  the  other  (1.634)  and  the  result  is  1.073, 
which  is  the  refractive  index  of  the  lens  as  it  is  enclosed  in  the 
two  plates  of  glass. 

In  order  to  ascertain  its  power  we  have  the  following  pro- 
portion : 

X  :  8  D  :  :  .073  :  .523 
X  =  8  X  .073  =  1.11  D. 
.523 

Therefore  the  power  of  this  8  D.  lens  inside  the  enclosing 
plates  of  glass  has  been  reduced  to  1.11  D. 


An  8  D.  lens  is  decentered  4.5  mm.;  what  is  the  prismatic 
effect  of  the  deviation  in  prism  diopters? 

The  unit  of  measurement  is  1  p.  d.  for  each  diopter  of 
refractive  power,  when  decentered  10  mm. 

An  8  D.  lens  decentered  10  mm.  =  8  p.  d. 
"       "        "             "             1  mm.  =  .8  p.  d. 
"       "        "             "             4.50  mm.  -  3.6  p.  d. 
The  prismatic  effect  of  an  8  D.  lens  decentered  4.5  mm.  is 
3.6  p.  d.  

An  object  is  placed  9  inches  in  front  of  a  lens  and  an  image  of 
this  object  is  formed  at  18  inches  from  the  lens  on  the  other  side; 
ivhat  is  the  principal  focus  of  the  lens  in  inches?  Make  the  calcula- 
tion. 

0    ^    /        / 


or  substituting  figures 

The  principal  focus  of  this  lens  is  6  inches. 


9   ^  18 


How  are  rays  of  light  reflected  from  piano,  concave  and  convex 
mirrors? 

No  matter  whether  the  surface  is  piano,  concave  or  convex, 
the  laws  of  reflection  are  always  the  same,  viz. : 


34  State  Board  Examinations 

The  angles  of  reflection  and  incidence  are  equal. 

The  incident  and  reflected  rays  are  always  in  a  plane  per- 
pendicular to  the  reflecting  surface. 

In  the  case  of  a  plane  mirror  the  incident  ray  is  reflected  in 
the  opposite  direction  at  the  same  angle. 

In  the  case  of  a  concave  mirror  the  rays  are  reflected  accord- 
ing to  the  same  law,  and  if  parallel  are  converged  to  a  point 
which  is  the  principal  focus  of  the  mirror,  and  is  approximately 
half  its  radius  of  curvature. 

In  the  case  of  a  convex  mirror  the  rays  of  light  according 
to  the  same  law  are  reflected  divergently. 


The  index  of  a  certain  substance  is  stated  to  he  1.564;  what 
is  the  meaning  of  this  statement? 

By  the  index  of  refraction  of  a  substance  is  meant  its  relative 
density  or  the  comparative  length  of  time  required  for  light  to 
travel  a  definite  distance  in  different  substances.  The  greater 
the  density  the  slower  the  velocity,  and  the  smaller  the  angle  of 
refraction. 

The  index  of  refraction  is  found  by  dividing  the  sine  of  the 
angle  of  incidence  by  the  sine  of  the  angle  of  refraction.  In 
this  particular  case  the  result  was  1.564  which  has  been  deter- 
mined wdth  reference  to  air,  the  index  of  which  is  regarded  as 
unity.  Or,  in  other  words,  the  lessened  rapidity  with  which 
light  passes  through  this  substance  as  compared  with  air,  the 
ratio  being  1  to  1.564. 

When  a  ray  of  light  passes  from  a  denser  to  a  lighter  medium, 
which  way  is  the  ray  bent? 

According  to  the  laws  of  refraction  in  passing  from  a  dense 
to  a  rare  medium,  as  from  glass  into  air,  if  the  ray  is  oblique  it 
is  bent  from  the  perpendicular.  If  the  ray  impinges  upon  the 
second  medium  at  right  angles  it  passes  unrefracted. 


An  object  is  24  inches  high  and  it  is  60  inches  from  a  lens; 
the  image  of  this  object  is  10  inches  from  the  lens;  what  is  the  height 
of   the   image? 


Theoretic  Optics  35 

If  i  is  size  of  image,  o  size  of  object,  d  i  distance  of  image, 
and  d  o  distance  of  object,  the  proportion  is  expressed  as  follows: 

i  :  0  ::  d  i  :  d  o 
Substituting    the    figures    in    the    above    question    we    have 
X  :  24  ::  10  :  60 

V      240       ... 
X  =  -77-  =  4  inches. 
oU 


An  image  formed  by  a  certain  lens  is  5  mm.  wide  and  at  a  distance 
of  200  mm.  from  the  lens.  The  object  is  4  meters  distant;  how  wide 
is  it? 

Using  the  same  proportion  and  substituting  figures  we  have 
5  mm.  :  X  ::  200  mm.  :  4  m.  or  4000  mm. 
V       20000  . 

This  is  equivalent  to  10  cm.  or  1/10  meter. 


The  distance  of  an  object  from  a  certain  lens  is  24  feet  {288) 
inches;  the  distance  of  the  image  of  this  object  from  the  lens  is  6  inches 
on  the  same  side  of  the  lens  as  the  object;  ivhat  is  the  principal 
focus  of  the  lens? 

If  we  assumed  that  the  rays  from  20  feet  and  beyond  were 
parallel  then  these  rays  from  24  feet  forming  an  image  at  6  inches 
would  indicate  this  distance  as  the  principal  focus,  and  as  the 
image  is  on  the  same  side  of  the  lens  as  the  object,  it  must  be 
virtual  and  the  lens  concave. 

To  work  it  out  accurately  we  use  this  general  formula: 

O  I  f 

in  which  0  represents  the  distance  of  the  object,  i  the  distance 
of  the  image,  and  /  the  principal  focus  of  the  lens. 
Substituting    figures    we    have 

In  this  case  the  focus  is  .12  or  1/8  inch  closer  than  if  we  assumed 
the  rays  to  be  parallel. 


36  State  Board  Examinations 

The  principal  focus  of  a  certain  plus  lens  is  10  inches;  the 
object  is  placed  20  inches  from  the  lens;  where  will  the  image  of  the 
object  be  found? 

0  ~   W       20        20 
Image  of  object  will  be  found  at  20  inches. 


An  object  is  ^2  meter  from  a   -\-   6  D.  lens;  where  will  the 
image  be? 

Using  the  regular  formula  and  substituting  values, 


—  =  6  D.  -  2  D.  =  4  D. 


1       1 

—  =—r   meter. 
0        4 


The  image  will  be  ^  meter  from  the  lens. 


A  certaiji  plano-convex  lens  has  a  principal  focus  of  40  mm. 
and  the  index  of  refraction  of  the  glass  is  1.620;  what  is  the  radius 
of  curvature  of  the  convex  surface? 

The  rule  is  that  the  focus  multiplied  by  index  of  refraction 
less  unity  equals  radius  of  cur\'ature. 
Substituting  values 

40  (1.620  -  1)  =  40  X  .620  =  24.8. 
The  radius  of  curvature  of  the  convex  surface  is  24.8  mm. 


A  certain  lens  has  an  index  of  1.500,  one  surface  being  on  a 
radius  of  12  inches  and  the  other  on  a  radius  of  24  inches;  what 
will  be  the  principal  focus  of  the  lens? 

Inasmuch  as  the  refractive  index  is  exactly  1.50,  and  no 
more,  we  may  say  that  the  focal  length  of  a  plano-convex  lens  is 
equal  to  twice  the  length  of  its  radius.  Therefore,  the  focal 
length  of  the  12-inch  surface  is  24  inches,  and  of  the  24-inch 
surface,  48  inches. 

Then  applying  our  formula  we  have 

24  "^48  "TS  '  °^  16 
That  is,  the  principal  focus  is  16  inches  from  the  lens. 


Theoretic  Optics  37 

In  transposition  of  lens  poiver  does  the  cylinder  ever  change 
in  value?     What  is  the  reason? 

In  transposition  of  sphero-cylindrical  lenses  the  number  of 
the  cylinder  must  always  remain  the  same,  although  there  is  a 
change  in  its  sign  and  in  the  position  of  its  axis.  The  amount 
of  the  cylinder  cannot  be  changed  because  it  represents  the  degree 
of  astigmatism  or  the  difference  in  power  between  the  meridians 
of  least  and  greatest  curvature.  This  is  an  important  point  for 
the  student  to  remember,  because  if  he  loses  sight  of  it  he  soon 
falls  into  error  in  working  out  problems  in  transposition. 


Hoiv  is  it  possible  to  measure  the  strength  of  a  plus  lens  without 
using  either  neutralizing  lenses  or  a  lens  measure? 

By  measuring  its  focal  distance.  By  allowing  the  rays  from 
an  object  at  least  20  feet  distant,  as  a  tree,  or  a  house,  or  a  sign, 
to  pass  through  the  lens  and  form  an  image  on  a  screen.  The 
lens  is  slowly  moved  closer  to  and  farther  from  the  screen  until 
the  image  is  found  to  be  the  most  distinct,  and  then  the  distance 
of  the  lens  from  the  screen  will  represent  the  principal  focal 
distance  of  the  lens,  which  can  then  be  converted  into  diopters 
to  show  its  refractive  power. 


Object  is  14  inches  high  and  its  distance  from  a  2-inch  focus 
concave  mirror  is  40  inches;  what  is  the  height  of  the  image? 

First  we  must  find  the  distance  of  the  image.  If  distance  of 
object  is  40  inches  from  a  2-inch  concave  mirror  the  distance  of 
image  is  found  by  the  following  formula: 

J 1    ^    19 

2         40   ~    40 

That  is,  image  is  at  2  2/19  inches. 

Now  then,  in  order  to  find  the  height  of  image,  we  make  use 
of  the  usual  proportion 

X  =  14/19  of  an  inch,  which  is  the  height  of  the  image. 


38  State  Board  Examinations 

Object  is  80  inches  high,  its  image  is  2  inches  high,  the  mirror 
being  convex.  The  distance  of  the  object  from  the  mirror  is  80 
inches;  what  is  the  principal  focus  of  the  mirror? 

If  an  object  is  80  inches  high  and  its  distance  is  80  inches, 
then  if  the  image  is  2  inches  high  its  distance  will  be  2  inches. 

Having  the  distance  of  the  object  (80  inches)  and  the  distance 
of  the  image  (2  inches),  the  principal  focus  of  the  mirror  is  found 
by  the  following  formula: 

11  39  .  2   .    , 


A  3-inch  concave  mirror  forms  an  image  of  a  certain  object, 
the  object  lyi  feet  high  and  the  image  7^  inches  high.  How  far 
away  is  the  object  from  the  mirror? 

We  have  the  size  of  object  and  the  size  of  image,  and  in 
order  to  find  distance  of  object,  we  must  work  out  the  distance 
of  image  as  the  third  proportion. 

The  object  is  twelve  times  the  size  of  the  image,  therefore 
the  distance  of  object  must  be  twelve  times  that  of  image.  The 
whole  focal  distance  is  3  inches,  of  which  ^~/iq  represents  distance 
of  image  and  Via  distance  of  object. 

1.1         1 
13  °^  T  =  3-9 

that  is,  39  inches  is  the  distance  of  object  from  the  mirror. 

This  can  be  proven  by  finding  the  distance  of  image  as  ^%Q, 
and  then  using  formula: 


J^       12  ^  JJ       \_ 
39  "^  39  ~  39  °''  3 


or  3-inch  focus. 


An  object  which  is  2  feet  wide  is  at  a  distance  of  8  feet  from  a 
4  D.  convex  mirror;  what  is  the  width  of  the  image? 

In  a  convex  mirror  the  focus  is  negative,  but  otherwise  the 
rules  governing  the  calculations  of  conjugate  foci  are  the  same 
as  with  a  concave  mirror. 


Theoretic  Optics  39 

In  this  case  we  have  the  distance  of  the  object  and  the 
principal  focal  distance  of  the  mirror,  and  we  get  the  distance 
of  the  image  by  the  following  formula: 

_  J 1_  ^ 1_ 

10       96  3 

9— 
53 

The  image  is  virtual  and  9%3  inches  behind  the  mirror. 

Now   then  we   find   the  width   of   the  image  by   the  following 

proportion : 

96  :  24  :  :  9  3/53  :  X 
Or  as  the  size  of  the  object  is  %  of  its  distance,  so  the  size 
of  the  image  will  be  ^  of  its  distance. 

X   =  yi  of  9  3/53   =   2  14/53  inches 
That  is,  the  image  will  have  a  width  of  2^%3  inches. 


An  object  which  is  12  inches  in  diameter  is  40  feet  from  a 
concave  mirror.  The  image  of  the  object  formed  by  the  mirror 
is  4  inches  in  diameter.  On  what  radius  is  the  mirror  surface 
formed? 

In  the  first  place  we  find  the  distance  of  the  image  by  the 
following  proportion: 

Size  Object     Distance  Object     Size  Image     Distance' Image 
12  in.       :      480  in.      :       :     4  in.  :     X 

-.         480X4       ._.     , 
X  =  -r =  160  inches 

Having  the  distance  of  the  object  and  the  distance  of  the 
image,  we  find  the  principal  focal  distance  by  the  following 
formula: 

O  1  I 


Substituting  figures 


480  "^  160       480  °''  120 


120  inches,  or  10  feet  is  the  focus  of  the  mirror. 

And  as  the  radius  of  curvature  of  a  concave  mirror  is  twice 
the  principal  focus,  in  this  case  the  radius  on  which  the  mirror 
surface  is  formed  must  be  20  feet. 


40  State  Board  Examinations 

An  object  is  20  feet  from  a  convex  mirror.  Its  height  is  six 
times  as  great  as  the  height  of  its  image;  what  is  the  principal 
focus  of  the  mirror? 

If  the  height  of  the  image  is  1/6  the  height  of  the  object, 
then  the  distance  of  the  image  must  be  1/6  the  distance  of  the 
object;  this  would  give  us  40  inches  as  the  distance  of  the  image. 
The  distance  of  the  object  being  240  inches  and  of  the  image 
40  inches,  we  find  the  principal  focus  of  the  mirror  by  the  follow- 
ing formula,  always  remembering  that  in  a  convex  mirror  the 
focus  is  negative.          1  1    _     ■S     _    1 

40  ~  240  "  ~Ub   ~   48" 

48  inches  is  the  principal  focus  of  the  convex  mirror. 


What  is  the  radius  of  curvature  of  the  second  surface  of  a 
lens,  of  uhich  the  first  surface  has  a  radius  of  curvature  of  10  cm., 
the  principal  focus  of  the  entire  lens  being  25  cm.,  and  the  index 
of  refraction  being  1.5? 

If  the  radius  of  curvature  of  the  first  surface  of  the  lens  is 
10  cm.,  its  focal  length  would  be  twice  that  of  the  radius,  or  20 
cm.,  which  is  equivalent  to  a  dioptric  power  of  -f  5  D.  The 
principal  focus  of  the  entire  lens  is  25  cm.,  which  is  equivalent 
to  +  4  D.  Hence  the  dioptric  power  of  the  second  surface  of 
the  lens  must  be  —  1  D.,  which  would  correspond  to  a  focal 
length  of  100  cm.  and  a  radius  of  50  cm. 


An  object  3  inches  in  diameter  is  placed  in  front  of  a  concave 
mirror  at  such  a  point  that  its  image  is  formed  4  inches  from  the 
mirror,  the  diameter  of  the  images  being  y^  inch;  what  is  the  focus 
of  the  mirror? 

In  this  example  the  distance  of  the  image  is  4  inches  and  its 
size  ^  inch;  that  is,  the  distance  is  eight  times  the  size,  therefore 
the  distance  of  the  object  would  be  eight  times  its  diameter; 
the  latter  being  3  inches,  the  former  would  be  24  inches. 

Then  we  find  the  focus  of  the  mirror  by  the  usual  formula: 

1,1         7        1 

o  1  f  3_ 

7 
3  3/7  inches  is  the  focal  distance  of  the  mirror. 


Theoretic  Optics  41 

Transpose    the  following    to    tivo  forms    of   sphero-cylinders: 
+  /  cyl.  ax.  90°  ivith  1  cyl.  ax.  180°. 

+  1  D.  sph.  C  -  2  D.  cyl.  ax.  180°,  and 
-  1  D.  sph.  C  +  2  D.  cyl.  ax.    90° 


When  a  ray  of  light  passes  through  a  denser  medium  than 
air — a  piece  of  glass  for  instance — ayid  it  is  apparently  bent  or 
refracted  from  a  straight  line,  luhy  does  it  not  continue  in  the  same 
course  after  emerging  from  the  glass  that  it  assumes  while  passing 
through  the  glass?  Why  does  it  change  hack  to  the  same  angle  as 
before  entering  the  glass? 

Because  it  is  subject  to  the  laws  of  refraction,  and  hence 
in  passing  from  a  rare  to  a  dense  medium,  as  from  air  into  the 
piece  of  glass,  it  is  bent  toward  the  perpendicular;  and  in  passing 
from  a  dense  to  a  rare  medium,  as  when  it  emerges  from  the 
glass  into  air,  it  is  bent  from  the  perpendicular.  The  amount  of 
bending  in  each  case  is  equal,  and  hence  the  emergent  ray  is 
parallel  to  the  entering  ray. 

A  certain  lens  has  one  surface  convex  on  a  radius  of  four 
inches,  and  the  other  surface  convex  on  a  radius  of  ten  inches;  index 
of  refraction  1.60;  what  is  the  power  of  the  lens? 

The  focal  distance  of  each  surface  is  found  by  dividing  the 
radius  of  curvature  by  the  index  of  refraction,  less  one. 
4  4 


(1.60  -  1)         .60 


=  6  2/3  =  6D. 


^^  =    777    =  16  2/3  =  2. SOD 


(1.60  -  1)        .60 

6  D.  +  2.50  D.   =    +  8.50  D.  approximately  the  power  of  the 
lens. 


Why  is  it  that  as  a  lens  is  moved  from  side  to  side  a  distant 
object  seen  through  the  lens  seems  to  have  a  movement  of  its  own? 

Because  at  every  point  except  at  its  optical  center  the 
lens  will  show  a  prismatic  effect,  and  because  the  effect  of  a 
prism  is  to  cause  displacement  in  the  direction  of  its  apex.     In  a 


42  State  Board  Examinations 

lens  the  prismatic  effect  increases  from  the  center  to  the  periphery, 
and  hence  as  a  lens  is  moved  from  side  to  side  and  the  visual 
line  passes  through  the  lens  at  different  points  from  center  to 
periphery  the  prismatic  power  of  the  lens  comes  into  evidence 
and  causes  displacement.  As  the  lens  is  kept  moving  the  dis- 
placement shows  itself  as  a  movement  of  the  object,  which  in 
concave  lenses  is  in  the  same  direction,  and  in  convex  lenses 
opposite. 

In  what  direction  relative  to  each  other  do  rays  of  light  travel 
when  first  leaving  a  luminous  point? 

Divergently. 


What  effect  do  the  following  have  upon  parallel  light:  Convex 
sphere,  concave  sphere,  plano-convex  cylinder? 

Convex  sphere  converges  to  a  focal  point;  concave  sphere 
diverges  as  from  a  focal  point,  and  convex  cylinder  converges  to 
a  focal  line. 

What  three  things  happen  to  a  ray  of  light  incident  on  a  glass 
surface?  Refraction  (if  the  surface  is  curved),  reflection  and 
absorption. 

State  a  rule  for  the  transposition  of  a  compound  to  its  equivalent 
form  which  will  apply  to  both  minus  and  plus  forms  of  compoimds. 

The  new  sphere  is  obtained  by  the  algebraic  addition  of  the 
sphere  and  cylinder,  and  the  new  cylinder  retains  the  number 
of  the  old  one  but  changes  its  sign  and  axis. 


What  is  the  dioptric  power  of  a  plus  lens  with  a  focus  of  984 
inches,  the  index  of  refraction  being  1.742? 

In  a  case  where  the  radius  of  curvature  is  given  we  must 
know  the  index  of  refraction  in  order  to  figure  out  the  focal 
distance  of  the  lens.  But  in  a  question  like  this,  where  the 
focal  distance  is  given  with  a  desire  to  transpose  it  into  diopters, 
the  index  of  refraction  is  not  taken  into  account,  but  we  simply 


Theoretic  Optics  43 

divide  the  inch  number  into  40  and  the  result  will  be  .04  D.,  or 
approximately  1/25  of  a  diopter. 


What  is  the  radius  of  curvature  for  the  two  surfaces  of  a  -\-  3  D. 
lens  with  a  —  9  D.  surface  on  the  inner  side,  index  1.57? 

If  the  concave  surface  of  this  +  3  D.  lens  is  —  9  D.  the 
convex  surface  is  +  12  D. 

In  this  case  where  the  index  is  1.57  we  solve  the  problem  as 
follows : 

3.33  X  (1.57  -  1)  =  1.89  inches 
4.50  X  (1.57  -  1)  =  2.56  inches 


To  find  the  radius  of  curvature  for  the  surface  of  a  lens  we 
are  told  to  deduct  unity  from  the  index  of  refraction;  what  does 
this  mean,  and  give  an  example  that  will  apply  in  practice? 

If  the  index  of  refraction  is  1.54  and  we  deduct  unity,  there 
would  be  left  .54,  which  is  the  excess  above  unity  and  the  amount 
in  which  we  are  interested. 

Suppose  the  focal  length  of  the  lens  was  ten  inches,  the 
problem  would  be  focal  length  multiplied  by  index  of  refraction 
less  unity  equals  radius  of  curvature,  or  10  X  (1.54  —  1)  =  10  X 
.54  =  5.4.  In  this  case  if  the  focal  length  is  ten  inches  and  the 
index  of  refraction  1.54  the  radius  of  curvature  is  5.4  inches. 


What  is  the  fundamental  reason  for  light  being  refracted  as  it 
passes  from  one  substance  into  another? 

Because  of  the  difference  in  the  density  or  index  of  refraction 
of  the  two  substances.  If  light  would  pass  from  one  substance 
into  another,  both  of  the  same  density,  there  would  be  no  refrac- 
tion. As  the  density  of  a  substance  increases,  the  velocity  of 
light  is  diminished  and  then  refraction  takes  place. 


Find  the  radius  of  curvature  of  a  lens  for  its  two  surfaces, 
each  surface  to  be  alike  and  each  to  measure  one  diopter.  Index  of 
glass,  1.632. 


44  Stale  Board  Examinations 

Multiply  the  focal  length  by  twice  the  index  of  refraction 
less  one.     In  this  case  where  the  two  surfaces  each  measure  one 
diopter  the  focal  length  of  the  lens  is  twenty  inches. 
The  problem  is 

20  X  2  (1.632  -  1) 
or, 

20  X  1.264  =  25.28  inches, 
which  is  the  radius  of  curvature. 


How  would  you  transpose  the  following  cross-cylinder  into  an 
equivalent  sphero-cylinder  witlwut  using  a  mathematical  formula 
for  the  same:   -\-  .75  cyl.  axis  120°  combined  with  —  2  cyl.  axis  60°? 

I  would  take  these  two  cylinders  from  the  trial  case  and 
place  them  in  the  positions  indicated  in  the  trial  frame.  Then  I 
would  look  through  this  combination  at  a  straight  line  and 
locate  the  two  principal  meridians,  which  I  would  then  proceed 
to  neutralize  with  convex  or  concave  spheres.  Or,  in  other 
words,  inasmuch  as  this  obliquely  crossed  cylinder  is  equivalent 
to  a  sphero-cylinder,  I  would  neutralize  the  combination  in  the 
same  way  that  any  sphero-cylinder  would  be  neutralized.  Then 
the  opposite  of  this  neutralizing  combination  would  be  the 
transposition  desired. 

With  a  candle  flame  one  meter  from  two  -]-  3  D.  lenses  placed 
13  inches  apart,  where  should  the  screen  be  placed  to  receive  a  perfect 
image  of  the  candle  flame? 

The  divergent  rays  from  the  candle  40  inches  away  after 
being  refracted  by  the  first  lens  are  converged  to  a  point  20 
inches  on  the  other  side  of  the  lens,  but  on  their  way  they  meet 
the  second  lens  placed  13  inches  from  the  first,  and  they  are 
then  convergent  to  a  point  7  back  of  the  second  lens  (20  —  13  = 
7).  The  eflfectivity  then  of  the  first  lens  in  the  plane  of  the  second 
lens  is  that  of  1  '7,  or  the  effect  is  the  same  as  if  a  7-inch  lens  was 
placed  in  contact  with  the  second  lens,  and  the  screen  to  receive 
a  perfect  image  of  the  flame  would  be  placed  at  4  11/20  inches 
being  found  as  follows: 

1     ,     1    20      ,   11  .    . 


Theorelic  Optics 


45 


If  Fr  =  resultant  focus, 
If  Fi  =  focus  of  first  lens, 
If  F2  =  focus  of  second  lens. 

If  d  =  distance  between  the  two  lenses,  then  the  effective  focal 
distance  is  found  by  the  following  formula: 

(F,  -  d)  F, 


Fr  = 

Substituting  figures  we  have 
(20  -  13)       13 


Fr  = 


20  +   13 


13 


Fi  +  F. 


7    X    13  =  91        ,  11  .     , 
i3   -  13   =20  =  ^2"0'"^^^^ 


What  is  the  rule  to  figure  the  curvatures  of  the  surfaces  of  lenses? 


Fig.  9.     (See  next  page) 


Focus  multiplied  by  index  of  refraction  less  unity  —  radius 
of  curvature. 

For  instance,  take  a  20-inch  lens  of  an  index  of  refraction 
of  1.62. 

20  (1.62  -  1)  =  12  4/10  inches. 

Or  if  we  wished  to  use  the  metric  system  we  would  say  that 
with  an  index  of  refraction  of  1.62  the  radius  of  curvature  for  a 
1  D.  surface  is  62  cm.  and  for  a  2  D.  surface  31  cm.,  which 
corresponds  to  the  answer  of  12  4/10  inches  found  above. 


46  SUilc  Board  Examinations 

What  happens  zchen  light  strikes  a  polished  opaque  stirface 
and  a  polished  transparent  surface? 

When  light  falls  upon  a  polished  opaque  surface  it  is  prac- 
tically all  reflected.  When  it  falls  upon  a  polished  transparent 
surface  it  is  nearly  all  transmitted,  although  there  is  some 
reflection. 

What  is  meant  by  index  of  refraction?  Give  example  to  find 
relative  index  of  water. 

Commonly  we  understand  it  to  be  the  refractive  or  bending 
power  of  a  medium  as  compared  with  air,  which  is  standard,  and 
the  index  of  which  is  unity.  The  index  of  refraction  depends 
upon  the  relative  density  of  a  substance  or  the  comparative 
length  of  time  required  for  light  to  travel  a  definite  distance 
in  different  substances.  The  greater  the  density  the  slower  the 
velocity  and  the  more  the  refractive  power. 

In  order  to  find  the  index  of  refraction  of  any  substance  as 
compared  with  air  we  divide  the  sine  of  the  angle  of  incidence 
by  the  sine  of  the  angle  of  refraction.  (See  Fig.  9  on  preceding 
page.) 

Let  A  B  he  the  refracting  surface  separating  air  from  water. 
Let  C  D  be  a.  ray  incident  on  the  surface  at  the  point  D,  to  which 
the  line  E  D  F  is  the  perpendicular.  The  C  D  E  is  the  angle  of 
incidence  and  G  D  F  is  the  angle  of  refraction.  Then  £  C  is 
the  sine  of  the  angle  of  incidence  and  G  F  the  sine  of  the  angle 
of  refraction. 

We  divide  the  sine  of  the  angle  of  incidence  (4)  by  the  sine 
of  the  angle  of  refraction  (3),  and  the  answer  is  4/3,  or  1  1/3,  or 
L33,  which  is  the  index  of  refraction  of  water  as  compared  with 
air. 

When  does  a  real  image  produced  by  a  plus  lens  change  to  a 
negative  image? 

When  the  object  is  closer  to  the  lens  than  its  principal  focal 
distance  the  rays  will  emerge  divergently  and  the  image  will  be 
a  negative  one. 

What  is  the  rule  for  the  transposition  of  a  sphero-cylinder 
into  its  equivalent  form? 


Theoretic  Optics  47 

The  new  sphere  is  obtained  by  the  algebraic  addition  of  the 
sphere  and  cylinder  of  the  old  combination. 

The  new  cylinder  retains  the  same  number  or  dioptric  value 
as  the  old  one,  but  there  is  a  change  of  sign  and  axis. 


If  a  +  4  D.  lens  is  so  placed  in  relation  to  light  that  it  forms 
an  image  of  the  light  100  feet  away,  what  is  the  relative  size  of  object 
and  image? 

If  the  image  is  formed  at  a  distance  of  1,200  inches  from  a 
ten-inch  lens,  then  the  distance  of  the  object  is  found  by  the 

following  equation : 

J 1_   ^    119^ 

10         1200    ~    1200 

If  the  distances  of  image  and  object  are  as  1  to  119,  the 
relative  sizes  will  be  in  the  same  proportion. 


What  is  the  radius  of  curvature  of  a  double  convex  lens  of  5  D. 
of  power,  the  refractive  index  of  the  glass  being  1.542? 

When  glass  has  a  refractive  index  of  1.50  the  radius  of 
curvature  of  a  biconvex  lens  and  its  focal  distance  are  equal. 

But  in  this  case  where  the  index  is  1.542  the  radius  of  curva- 
ture of  this  eight-inch  focus  lens  is  8*""iooo  inches,  as  found  by  the 
following  formula : 

8X2  (1.542  -  1)  =  8  X  1.084  =  8.672 


What  is  the  refractive  index  of  a  piano  lens  of  Z  D.,  the  radius 
of  curvature  being  25  cm.?    How  do  you  make  the  calculation? 

We  divide  the  focus  into  the  radius,  as  25  cm.  divided  by 
50  cm.  (the  focal  length  of  a  2  D.  lens)  equals  .50.  This  being 
the  amount  above  unity,  the  index  of  refraction  is  1.50. 


What  is  the  focal  length  of  two  lenses  placed  in  contact  whose 
powers  are  -\-  3  D.  and  +  5  D.? 

The  two  lenses  would  be  equivalent  to  a  +  8  D.  lens  with  a 
focal  length  of  five  inches. 


48  Slalc  Board  Examinations 

Transpose  the  Jollouing  so  as  to  eliminate  spheres: 

(a)  +  5  D.  sphere  ^   -  4  D.  cyl.  axis     10° 

(b)  -\-  4  D.  sphere  =   -  4  D.  cyl.  axis    120° 

(a)  In  this  case  we  can  eliminate  the  sphere  only  by  trans- 
posing into  a  cross-cylinder,  as  follows: 

+  1  D.  cyl.  axis  10°  =  -f  5  D.  cyl.  axis  100° 

(b)  In  this  case,  where  the  sphere  and  cylinder  have  the 
same  value,  the  sphere  can  be  eliminated  by  transposition  into 
a  piano  cylinder,  as  follows: 

+  4  D.  cvl.  axis  30° 


Transpose  the  following  sphere  cylinder  to  its  equivalent  form 
and  explain  how  you  do  it: 

-\-  1  D.  sphere  =   -  .50  D.  cyl.  axis  120° 

The  new  sphere  is  obtained  by  the  algebraic  addition  of 
the  sphere  and  cylinder,  as  —  .50  added  to  +  1  =  -f  .50  D.,  which 
is  the  new  sphere. 

The  new  cylinder  has  the  same  value  as  the  old  one,  but 
its  sign  and  axis  changes  from  —  .50  D.  to  +  .50  D.  and  from 
axis  120°  to  axis  30°. 

The  completed  transposition  is:  -j-  .50  D.  =  +  -50  D.  cyl. 
axis  30°. 

Define  (a)  a  ray  of  light;  (b)  a  pencil  of  light. 

(a)  The  smallest  subdivision  of  light  traveling  in  a  straight 
line  and  perpendicular  to  a  wave  front. 

(b)  A  bundle  of  light,  cone-shaped  and  composed  of  con- 
vergent or  divergent  rays. 


When  light  falls  upon  a  transparejit  plate,  what  is  the  incident 
ray  and  which  is  the  emergent  ray? 

The  incident  ray  is  that  which  strikes  the  plate  after  leaving 
the  luminous  point.  The  emergent  ray  is  that  which  leaves  the 
plate  after  having  passed  through  it. 


What  three  things  may  happen  to  light  when  it  falls  on  a  surface? 


Theoretic  Optics  49 

Reflected,  absorbed  and  transmitted  or  refracted. 


Are  rays  of  light  coming  from  an  object  plus  or  minus? 

Rays  of  light  coming  from  an  object  are  divergent  and 
might  be  considered  as  minus,  because  they  require  a  convex 
lens  to  overcome  the  divergence  and  make  them  parallel. 


What  are  the  conjugate  foci  of  a  lens? 

The  location  of  object  and  image  which  are  interchangeable. 


What  is  a  real  focus  and  what  is  a  virtual  focus?  Give  an 
example  of  each. 

A  real  focus  is  formed  by  the  actual  meeting  of  rays  after 
refraction  by  a  convex  lens  and  can  be  caught  on  a  screen. 

A  virtual  focus  is  formed  by  the  imaginary  continuation 
backward  of  divergent  rays,  as  in  the  case  of  a  convex  mirror. 


At  what  distance  from  the  surface  of  the  mirror  will  parallel 
light  he  focused,  if  the  radius  of  curvature  of  the  mirror  is  20  inches? 

The  principal  focal  distance  of  a  concave  mirror  is  approx- 
imately one-half  the  radius.  Therefore,  in  this  case,  where  the 
radius  is  20  inches,  parallel  rays  would  be  focused  at  10  inches. 


Transpose  the  following: 

(a)  -  3.25  O  -{-  1.50  cyl.  axis  45° 

(b)  -h     .75  O  -     .75  cyl.  axis  90° 

(a)  -  1.75  sph.  =   -  1.50  cyl.  axis  135' 

(b)  +  .75  cyl.  axis  180° 


What  is  the  combined  value  of-\-3,  —  l,-\-4,  —  6? 
Zero. 

From  —  2.50  take  away  +  3.25 
-  5.75. 


50  State  Board  Examinations 

Change  +  -i-  O  —  .25  cyl.  axis  50°  to  its  equivalent  sphero- 
cylinder. 

-  .12  C  +  .25  cyl.  axis  140°. 


Change  the  following  to  its  equivalent  periscopic  form: 
+  1.25  sph.  C:  -\-  1.25  cyl.  axis  120° 

+  2.50  D.  sph.  C  -  1.25  D.  cyl.  axis  30° 


Transpose  to  corresponding  sphero-cylinders: 
(a)   —  .50  C^  -\-  .75  cyl.  axis  15° 
lb)   +  .50  cyl.  axis  50° 

(c)  -\-  .50  C:  -  .75  cyl.  axis  45° 

(d)  -  .50  cyl.  axis  90° 

(a)  +  .25  D.  sph.  =   -  .75  D.  cyl.  axis  105' 

(b)  +  .50  sph.  C  -  .50  cyl.  axis  140° 

(c)  -  .25  sph.  C  +  .75  cyl.  axis  135° 

(d)  -  .50  sph.  C  +  .50  cyl.  axis  180° 


Does  the  speed  of  light  hear  any  relation  to  the  index  of  refrac- 
tion, and  if  so,  what? 

The  velocity  of  light  is  lessened  in  media  denser  than  air, 
the  decrease  in  speed  being  roughly  proportionate  to  the  density. 
The  velocity  of  light  in  the  first  medium  is  to  the  velocity  of 
light  in  the  second  medium  as  the  index  of  refraction  of  the 
second  medium  is  to  the  index  of  refraction  of  the  first  medium. 
Or,  in  other  words,  the  rate  of  progression  of  light  in  a  medium 
is  inversely  proportional  to  its  optical  density.  For  example, 
if  the  index  of  refraction  of  glass  was  1.50  or  3/2,  then  the  speed 
of  light  as  it  passes  from  air  into  this  glass  is  reduced  to  2/3. 


When  light  falls  vertically  upon  a  plane  glass  surface,  what 
change  is  produced,  if  any? 

The  light  would  pass  unrefracted,  the  only  change  being 
that  its  speed  would  be  reduced  to  two-thirds  approximately. 


How  can  the  existence  of  refraction  he  shown  with  a  penny 
and  a  cup  of  water? 


Theoretic  Optics  51 

The  penny  is  placed  at  the  bottom  of  the  cup,  with  the  eye 
of  the  observer  in  such  a  position  that  it  cannot  be  seen.  The 
cup  is  filled  with  water,  and  without  any  change  in  the  position 
of  the  eye,  the  penny  comes  into  view. 


In  what  way  does  a  light  loave  differ  from  a  ray  of  light? 

In  studying  the  transmission  of  light,  there  is  assumed  to 
be  a  disturbance  in  the  ether  which  exists  throughout  the  uni- 
verse, manifesting  itself  by  a  series  of  waves,  which  is  usually 
likened  to  the  familiar  example  afforded  by  throwing  a  stone 
into  a  pool  of  still  water.  Therefore  the  wave  has  a  circular  or 
spherical  front. 

A  ray  of  light  is  the  smallest  conceivable  line  of  light,  and 
may  be  regarded  as  a  straight  line  perpendicular  to  the  wave 
front. 

//  we  place  a  transparent  solid  in  a  transparent  liquid,  what 
is  essential  that  the  solid  may  be  entirely  invisible? 

Both  must  have  the  same  color  and  same  density,  or  in 
other  words,  the  same  index  of  refraction. 


When  are  two  points  conjugate  foci  and  when  not? 

Two  points,  one  on  each  side  of  a  lens,  are  conjugate  to 
each  other  when  the  rays  diverging  from  one  are  converged  to 
the  other;  or  when  one  occupies  the  position  of  the  object,  and 
the  other  that  of  the  image,  and  when  these  are  interchangeable. 


The  center  of  curvature  of  a  concave  refiectini  surface  is  one 
meter  distant;  what  is  the  power  of  the  mirror? 

Parallel  rays  striking  a  concave  surface  are  reflected  from 
it  convergently,  and  are  made  to  meet  at  the  principal  focus  of 
the  mirror,  which  is  just  one-half  the  radius. 

In  this  case  the  center  of  curvature  or  radius  is  one  meter, 
then  the  principal  focal  distance  is  half-meter  or  twenty  inches, 
which  would  indicate  the  power  of  the  mirror  to  be  2  D. 


52  State  Board  Examinations 

When  will  a  concave  mirror  not  form  a  real  focics? 

When  object  is  placed  at  the  principal  focal  distance  of  the 
mirror,  no  image  is  formed  because  the  rays  are  reflected  parallel. 

And  when  the  object  is  placed  closer  than  the  principal 
focal  distance,  the  focus  is  a  negative  one. 


Why  is  the  power  of  the  crystalline  lens  so  much  less  when 
it  is  in  position  in  the  eye  than  it  is  when  it  is  measured  outside  of 
the  eye? 

Inasmuch  as  the  refractive  power  of  a  convex  lens  is  increased 
as  it  is  moved  a  little  farther  from  the  eye,  the  power  of  the 
crystalline  lens  would  be  very  much  greater  if  placed  in  the 
position  of  spectacles  about  half-inch  in  front  of  eye  than  when 
it  is  in  situ. 

Then,  again,  when  the  crystalline  lens  is  in  position  in  the 
eye,  it  is  in  contact  with  the  aqueous  in  front,  with  an  index 
of  refraction  of  1.33,  and  the  vitreous  behind  with  the  same  index; 
whereas,  when  it  is  outside  of  the  eye  it  is  surrounded  by  air, 
with  an  index  of  1.00.  Therefore  there  is  less  refraction  in  the 
first  case  when  the  light  passes  from  a  medium  with  an  index  of 
1.33  into  one  with  an  index  of  1.43  (which  is  the  crystalline  lens), 
than  in  the  second  case  above  it  passes  from  a  medium  with  an 
index  of  1.00  into  one  with  an  index  of  1.43. 


What  is  the  difference  between  a  ray  of  light,  a  beam  of  light, 
and  a  wave  of  light? 

A  wave  of  light  represents  the  disturbance  in  the  ether 
when  light  is  in  motion;  a  ray  of  light  is  the  smallest  conceivable 
line  of  light  and  indicates  the  direction  in  which  the  light  travels; 
a  beam  of  light  is  a  collection  of  parallel  rays,  as  for  instance  a 
sunbeam. 

What  effect  do  lenses  have  upon  light  comiyig  from  an  object? 

Lenses  bend  oi  refract  the  light  and  bring  the  rays  to  a 
focus  and  thus  produce  an  image  of  the  object.  This  applies 
only  when  the  object  is  at  a  greater  distance  than  the  principal 


Theoretic  Optics  53 

focus  of  the  lens.  If  the  object  was  at  the  principal  focal  distance, 
the  rays  would  emerge  parallel;  if  closer  than  this,  they  would 
emerge  divergently,  and  in  neither  of  these  two  cases  would  an 
image  be  formed. 

What  is  the  cause  of  spherical  aberration  in  lenses? 

Spherical  aberration  is  caused  by  the  difference  in  refraction 
power  of  different  parts  of  the  lens,  as  a  result  of  which  the 
rays  of  light  passing  through  the  lens  do  not  all  come  to  a  focus 
at  the  same  point,  but  those  passing  through  the  periphery 
come  to  the  sooner  focus. 


What  is  the  cause  of  spherical  aberration  in  mirrors? 

On  account  of  the  spherical  curvature  of  a  mirror,  the  rays 
of  light  reflected  from  the  peripheral  portions  do  not  come  to  a 
focus  at  the  same  point  as  those  reflected  from  the  central 
portions. 

Does  the  speed  of  light  increase  or  decrease  when  it  passes 
from  air  to  glass,  and  what  is  the  change  in  the  speed  if  the  index 
of  refraction  of  the  glass  is  1.50? 

The  greater  the  density  of  a  medium  the  more  light  is 
retarded,  therefore,  as  it  passes  from  air  into  glass  its  speed  is 
decreased,  and  this  decrease  is  to  2/3  if  the  index  of  the  glass  is 
1.50. 


What  becomes  of  the  energy  of  light  when  it  is  absorbed? 

When  light  is  absorbed  it  ceases  to  exist  as  light,  and  it 
becomes  manifest  as  heat. 


How  can  the  deviating  power  of  a  1°  prism  at  20  feet  be  cal- 
culated? 

A  1°  prism  will  deviate  light  1  cm.  for  each  meter  of  distance. 
As  twenty  feet  is  equivalent  to  six  meters,  the  deviation  at  this 
distance  would  be  6  cm. 


54  State  Board  Examinations 

What  are  the  several  meanings  of  the  ivord  refractioji? 

Refraction  means  bending  and  has  reference  to  the  deviation 
of  rays  of  light  as  they  pass  from  a  medium  of  one  density  into 
a  medium  of  a  different  density,  as  for  instance  in  passing  from 
air  into  a  glass  lens  and  then  from  that  lens  into  air,  the  rays  are 
refracted  by  the  lens. 

The  refraction  of  the  eye  is  its  optical  condition,  or  the 
manner  in  which  it  acts  on  the  entering  rays,  whether  bringing 
them  to  a  focus  on  the  retina,  or  in  front  of  or  behind  it,  these 
rays  being  refracted  by  the  media  of  the  eye. 


What  relation  does  index  of  refraction  hear  to  speed  of  light? 

As  the  index  of  refraction  of  a  substance  increases  the  speed 
of  light  decreases. 

Hozv  far  must  a  convex  lens  of  3  inches  focal  distance  be  placed 
from  a  candle  in  order  that  it  may  produce  a  real  image  of  the  candle 
frame  three  times  as  large  as  the  flame  itself? 

Inasmuch  as  the  distance  of  the  object  is  to  the  distance  of 
the  image  as  the  size  of  the  object  is  to  the  size  of  the  image; 
therefore,  if  the  size  of  the  image  is  to  be  three  times  the  size  of 
the  object,  its  distance  must  be  three  times  the  distance  of  the 
object. 

Let  X  =  distance  of  object  and  3  X  =  distance  of  image, 
then 

4  X  =  1/3 

X  =  1/12 
3  X  =  1/12  or  1/4 
Therefore   the   candle   must   be   placed   4  inches   from   the 
lens  in  order  that  a  real  image  may  be  formed,  magnified  three 
times. 


A  parallel  beam  of  light  passes  through  a  convex  lens  of  power 
-\-  2  D.  and  which  is  3  inches  in  diameter.  What  is  the  size  of 
the  circular  patch  of  light  which  it  casts  on  a  screen  10  inches 
distant? 


Theoretic  Optics  55 

These  parallel  rays  of  light  will  be  brought  by  this  lens  to 
focal  point  at  a  distance  of  20  inches.  If  these  convergent  rays 
are  intercepted  by  a  screen  at  a  distance  10  inches,  which  is 
just  one-half  the  distance  between  the  lens  and  the  focus,  the 
patch  of  light  will  be  exactly  one-half  the  diameter  of  the  lens, 
that  is  1>^  inches. 

//  an  object  is  placed  12  inches  in  front  of  a  plus  lens  whose 
focal  length  is  6  inches,  where  will  the  image  he,  and  what  are  the 
two  points  called? 

Let  F  represent  focal  length  and  O  distance  of  object  and 
1  distance  of  image.    Then  the  standard  formula  is 

0^1         F 

If  any  two  of  these  quantities  are  known,  the  third  can  be 
found  by  this  formula.  In  this  case  the  distance  of  object  and 
focal  length  are  given,  and  in  order  to  find  distance  of  image  the 
formula  is 


or  substituting  figures 


F         0         1 


J 1_  ^  J_ 

6  12  12 


The  image  will  be  at  12  inches  and  the  two  points  are  called 
conjugate. 

If  the  eyes  of  fishes  focus  parallel  rays  of  light  when  in  the 
water,  what  would  he  the  refractive  conditions  of  such  eyes  when 
in  air? 

When  the  eyes  of  fishes  are  in  water  and  light  passes  from 
the  water  into  the  cornea,  there  is  no  refraction  because  both 
have  the  same  index  of  refraction,  viz.,  1.33.  But  when  light 
passes  from  air  with  an  index  of  1.00  into  the  cornea  with  an 
index  of  1.33,  the  rays  are  converged. 

Now  if  under  the  first  condition  parallel  rays  are  focused  on 
the  retina;  under  the  second  condition  they  would  be  focused 
in  front  of  the  retina;  or  in  other  words  the  refractive  condition 
in  air  would  be  myopic. 


56 


State  Board  Examinations 


A  thin  convex  lens  having  a  focal  length  of  3.5  inches,  is  placed 
in  contact  with  two  concave  lenses  having  respectively  focal  lengths 
of  7.8  inches  and  12.4  inches;  what  is  the  focal  Hength  of  the 
combination? 

We  think  the  simplest  way  would  be  to  transpose  these  focal 
lengths  to  dioptric  powers  and  then  make  the  necessary  calcula- 
tions. 

7.8  focal  length  =     5.05  dioptric  power 
12.4     "  "        =     3.17 

3.5     "  "       =  11.25 

Then  we  have  +  11.25  D.  placed  against  —  8.22  D.,  and 
the  resultant  dioptric  power  will  be  -f  3.03  D.,  which^has  a  focal 
length  of  13  inches. 

These  transpositions  are  made  by  dividing  into  39.37,  which 
are  the  number  of  inches  in  a  meter. 


What  is  the  value  expressed  in  a  single  lens  of  the  following? 
+  2.50  sph.   =  +  2.50  cyl.  axis    90° 


-  1.25     ' 

=   -  1.25    " 

'      90° 

+  4.00    ' 

=   -  1.00    " 

'     180° 

-  2.25     ' 

=   -  2.00    " 

'     180° 

-  3.00     ' 

=  +  1.00    " 

'       90° 

+  1.25     ' 

=   -  0.75    " 

'      90° 

In  order  to  get  the  proper  result  all  the  cylinders  must  have 
the  same  axis;   we  can  transpose  either  to  180°  or  90°. 

We  will  choose  the  latter  as  this  requires  only  two  transposi- 
tion.   Then  we  have 

+  2.50  sph.  =  +  2.50  cyl.  axis  90° 


-  1.25     ' 

=   -  1.25    " 

"     90° 

-f  3.00     ' 

=  +  1.00    " 

"     90° 

-  4.25     ' 

=  -f  2.00    " 

"     90° 

-  3.00     ' 

=  +  1.00    " 

"     90° 

+  1.25     ' 

=   -  0.75    " 

"     90° 

-  1.75  sph.  =  +  4.50  cyl.  axis  90° 
This  result  being  obtained  by  algebraic  addition. 


//  an  object  at  20  inches  from  a  convex  lens  has  an  image  20 
inches  on  the  other  side,  what  is  the  power  of  the  lens? 


Theoretic  Optics  57 

Rays  reaching  the  convex  lens  from  a  distance  of  20  inches 
would  call  for  a  convex  lens  of  2  D.  to  overcome  their  divergence, 
and  in  order  that  an  image  be  formed  at  20  inches  on  the  other 
side  of  the  lens,  the  rays  leaving  the  lens  must  have  such  con- 
vergence as  is  produced  by  a  convex  lens  of  2  D.  Therefore, 
in  order  to  accomplish  both  of  these  results  the  lens  must  have 
a  power  of  4  D. 

Or  if  O  is  distance  of  object,  and  1  is  distance  of  image,  and 
F  is  principal  focal  distance,  the  formula  is 


0^1  F 


or    substituting    numbers 


20  ^  20       20  °^  10 
Therefore  10  inches  is  the  focal  distance  of  the  lens. 


Why  ought  a  person  totally  immersed  in  water  to  wear  convex 
lenses  in  order  to  see  distinctly? 

In  order  that  refraction  may  take  place,  the  rays  must  pass 
from  a  medium  of  one  density  into  a  medium  of  a  different 
density;  as  long  as  they  continue  in  the  same  density  there  is 
no  refraction. 

Under  natural  conditions  light  passes  from  air  with  an 
index  of  1.00  into  the  cornea  with  an  index  of  1.33,  and  is  strongly 
refracted.  But  when  immersed  in  water,  light  passes  from  the 
water  with  an  index  of  1.33  into  the  cornea  with  the  same  index, 
and  without  refraction. 

Now,  inasmuch  as  the  refracting  power  of  the  cornea  is 
neutralized  by  the  water  in  contact  with  it,  distinct  vision  would 
be  impossible  unless  this  neutralization  of  power  is  compensated 
for  by  a  strong  convex  lens  in  front  of  the  eye. 


How  jar  mnst  a  —  9  D.  sphere  and  a  -\-  8  D.  sphere  be  placed 
from  one  another  in  order  to  neutralize  each  other?  Does  it  make 
any  difference  which  lens  is  in  front  of  the  other? 

In  order  to  produce  neutralization  these  two  lenses  must  be 
separated  by  the  distance  between  their  focal  lengths. 


58  State  Board  Examinations 

Approximately  the  focal  length  of  the  +  8  D.  lens  is  5 
inches  and  of  the  —  9  D.  lens,  4^  inches,  and  the  difference 
between  the  two  is  one-half  inch,  and  roughly  speaking  the 
distance  between  the  lenses  should  be  one-half  inch. 

A  more  accurate  way  is  to  reduce  to  centimeters  and  subtract. 

Q  r»  100        10=: 

8  D.  =  -3-  =  12.5  cm. 

o 

9D.  =  lf«  =  ll.lcm. 

The  difference  between  their  focal  lengths  is  1.4  cm. 

If  the  convex  lens  is  in  front  the  parallel  rays  would  be 
refracted  so  as  to  meet  at  12.5  cm.,  but  at  a  distance  of  1.4  cm. 
they  meet  the  concave  lens.  At  this  point  their  convergent  value 
is  reduced  to  (12.5  —  1.4  cm.)  11.1  cm.  and  as  the  concave  lens 
has  an  equivalent  value  in  divergence,  there  is  neutralization. 

If  the  concave  lens  is  in  front  parallel  rays  would  be  made 
to  diverge  as  if  from  11.1  cm.,  but  at  a  distance  of  1.4  cm.  they 
meet  the  convex  lens.  At  this  point  their  divergence  has  increased 
to  (11.1  cm.  -f  1.4  cm.)  12.5  cm.,  but  as  the  convex  lens  has  an 
equal  amount  of  convergence,  there  will  be  neutralization. 


A  thin  plano-convex  lens  made  of  dense  flint  glass,  having  an 
index  of  refraction  of  1.7,  has  a  radius  of  curvature  of  15  inches  for 
its  curved  surface;  how  can  you  find  its  focal  length? 

The  formula  is 

4=(i  +  f)<-» 

Or  to  express  it  in  every-day  language,  the  focal  distance 
equals  the  radius  of  curvature  of  the  first  surface  plus  the  radius 
of  the  second  surface,  and  their  sum  multiplied  by  the  index  of 
refraction  less  one. 

Substituting  figures  in  the  above  formula: 


F-(iV+i)  <'•'-'•> 


r°T5  xk'io'"^'*''"'^''' 


Theoretic  Optics  59 

What  is  the  formula  that  applies  to  the  conjugate  focal  distances 
of  a  spherical  mirror? 

Conjugate  foci  are  the  positions  occupied  by  the  object  and 
its  image.  They  are  interchangeable  and  when  the  object 
is  at  one,  the  image  must  be  at  the  other.  The  rays  diverging 
from  one  focus  are  converged  to  the  other. 

The  letter  F  is  used  to  represent  the  principal  focal  distance 

of  a  mirror,  and  its  reciprocal  (written  p)  would  indicate  its 
reflecting  power.  For  instance,  if  8  inches  was  the  principal 
focal  distance  of  a  mirror,  its  power  of  reflection  would  be  %. 

If  fi  be  used  to  represent  the  distance  of  the  object,  then 

its  reciprocal  (|^)  would  be  the  power  that  brings  parallel  rays 
to  a  focus  at  such  distance. 

If  fo  be  used  to  represent  the  distance  of  the  image  from 

the  mirror,  then  its  reciprocal  (f^  would  indicate  the  power 
which  causes  parallel  rays  to  meet  at  such  distance. 

With  a  concave  mirror  the  quantities  are  positive,  and  the 

full  power  of  the  mirror  (represented  by  p)  is  equal  to  the  sum 
of  the  powers  which  represent  the  distances  of  the  object  and 
image;  or  in  other  words,  the  reciprocal  of  the  principal  focal 
distance  is  equal  to  the  sum  of  the  reciprocals  of  any  pair  of 
conjugate  foci,  as  follows: 

F         fi   ^  f. 
or 

1 L  ^  i. 

F  fl      ~      f2 

This  is  one  of  the  most  important  formulae  in  optics.  If 
any  two  of  these  quantities  are  known,  the  third  can  always  be 
found. 

The  formula  is  universal  and  holds  good  for  all  spherical 
mirrors,  both  concave  and  convex,  and  also  for  lenses. 


In    what    other   ivay    may    the  formula  for   conjugate  focal 
distances  he  expressed? 

If  the  letter  A  be  used  to  represent  the  distance  of  the  object 


60  State  Board  Examinations 

from  the  principal  focus  and   the  letter  B  the  distance  of  the 
image,  then 

AB  =  F2 
or  in  other  words,  the  distance  of  the  object  multiplied  by  the 
distance  of  the  image  equals  the  square  of  the  principal  focal 
distance. 

Suppose  we  have  an  object  placed  6  inches  in  front  of  a 
concave  mirror  of  10  inches  focal  distance. 

The  formula  is 

J 1_   ^  J_ 

F  fl        ~       f2 

Substituting  figures  we  have 

10        6    ~        60  °''       15 

That  is  the  image  is  15  inches  behind  the  mirror. 

Using  the  second  expression  A  B  =  F2  we  have  by  substitut- 
ing figures: 

4  X  25  =  100 
and    100  being  the  square  of   10,  which  is  the   principal  focal 
distance. 


//  an  object  he  situated  at  sixty  inches  in  front  of  a  concave 
mirror  of  20  inches  focal  length,  where  will  the  image  he  found? 

Here  we  have  the  principal  focal  distance,  which  is  F,  and 
the  distance  of  the  object  which  is  fi.  Then  the  reciprocal  of 
the  latter  subtracted  from  the  reciprocal  of  the  former  will  equal 
the  reciprocal  of  the  distance  of  the  image,  as  per  the  following 
formula: 


Substituting    figures 


The  image  if  formed  at  a  distance  of  30  inches.  In  this  case 
30  inches  and  60  inches  are  conjugate  foci  in  respect  to  a  20- 
inch  concave  mirror,  so  that  if  the  object  is  situated  at  a  distance 
of  30  inches  its  image  will  be  formed  at  a  distance  of  60  inches. 


1 

1 

1 

F 

fi 

f2 

1 

20 

— 

1 
60 

= 

2 
60 

or 

1 
30 

Theoretic  Optics  61 

If  an  object  be  situated  at  sixty  inches  in  front  of  a  convex 
mirror  of  twenty  inches  focal  length,  where  will  the  image  be  found? 

Here  we  must  keep  in  mind  that  the  focal  distance  and 
power  of  a  convex  mirror  are  negative  quantities,  otherwise  the 
rules  governing  the  calculations  of  conjugate  foci  are  the  same 
as  with  a  concave  mirror.     Therefore  it  must  be  expressed 


or 


The  image  would  be  a  virtual  one  and  situated  15  inches 
behind  the  mirror. 

—  15  inches  and  60  inches  are  conjugate  to  each  other  with 
respect  to  a  20-inch  convex  mirror,  but  not  15  inches  and  60 
inches;  the  15  inches  is  a  minus  quantity.  If  the  rays  were 
convergent  to  a  point  15  inches  back  of  the  mirror,  on  striking 
this  20-inch  convex  mirror  their  convergence  would  be  so 
lessened  that  they  would  be  reflected  so  as  to  meet  at  a  point 
60  inches  in  front  of  the  mirror. 


1 

F 

1 
fi 

+ 

1 

f2 

1 
20 

1 
60  ~ 

:     — 

1 

15 

//  an  object  one  inch  in  diameter  is  placed  16  inches  in  front 
of  a  24-inch  mirror,  what  will  be  the  size  of  the  image? 

In  the  first  place  we  must  find  the  distance  of  the  image, 
for  which  we  used  the  regular  formula: 

A-l=f,  =   -1 
24        16         -  48 

The  image  would  be  virtual  and  at  a  distance  of  48  inches. 

Let  O  represent  the  size  of  the  object,  and  I  the  size  of  the 
image,  and  fi  the  distance  of  the  object  and  {2  the  distance  of 
the  image. 

Then  the  working  formula  is 
O  f.. 


f.  =  ' 


Substituting  figures 

1  X  48 


16  16 


=  3  inches. 


62  State  Board  Examinations 

The  size  of  the  image  is  3  inches. 

Or  we  can  get  the  result  by  the  proportion  given  above, 
X  :  1   ::  48  :  16 
X  =  3 


What  is  understood  by  Snellen's  Law  or  the  Law  of  Sines? 

This  has  reference  to  the  determination  of  the  index  of 
refraction  of  a  substance  as  compared  with  air,  and  depends  upon 
the  relation  of  the  angle  of  incidence  to  the  angle  of  refraction, 
being  expressed  in  the  following  formula: 

sin  i  ,  . 

-. =  /«  (a  constant) 

sin  r 

This  is  known  as  Snell's  Law,  in  honor  of  its  discov^erer, 
W.  Snell,  a  Holland  scientist,  who  died  nearly  three  hundred  years 
ago. 

The  direction  of  the  refracted  ray  is  not  the  same  as  that  of 
the  incident  ray,  but  there  is  a  definite  relation  between  these 
two  directions,  as  shown  by  the  law  above  mentioned,  which 
applies  to  any  case  where  a  ray  of  light  meets  the  di^•iding  line 
between  media  of  different  density,  as  between  air  and  glass,  air 
and  water,  etc. 

When  the  light  passes  from  a  medium  of  less  density  into 
one  of  greater  density,  it  is  bent  towards  the  perpendicular,  when 
it  follows  that  the  angle  of  refraction  is  less  than  the  angle  of 
incidence,  and  under  these  conditions  the  index  of  refraction  is 
greater  than  unity. 

When  light  passes  from  a  medium  of  greater  density  to  one 
of  less  density,  at  the  surface  of  separation  of  the  two  media, 
it  is  bent  away  from  the  perpendicular,  and  then  the  angle  of 
refraction  is  greater  than  the  angle  of  incidence,  under  which 
conditions  the  index  of  refraction  is  less  than  unity. 

Inasmuch  as  nearly  all  transparent  media  are  denser  than 
air,  their  refractive  indices  are  greater  than  unity,  as  shown  by 
their  deflection  of  light  towards  the  perpendicular. 


What  is  the  focal  distance  of  a  lens  with  an  index  of  refraction 
of  L54  and  its  two  surfaces  having  radii  of  8  inches  and  5  inches? 

Let  /i  represent  the  index  of  refraction  of  the  lens,  r  the  radius 


Theoretic  Optics  63 

of  curvature  of  the  first  surface,  and  r  the  radius  of  the  second 
surface;  then  the  power  of  the  first  surface  is  represented  by  the 
formula 

u     -     1 

r 
and  the  power  of  the  second  surface  by 

M   -   1 
r' 

and  the  total  power  of  the  lens  by 

M   -    1        M  -   1    ^  _l_ 
r  "^         r'  F 

or  it  may  be  written 

r       r' 
F 


(r  +  r'  )    {^i  -  i) 
Substituting  figures 

Both  surfaces  are  of  the  same  nature  and  the  focus  is  positive. 


What  is  the  focal  distance  of  a  lens  with  an  index  of  refraction 
of  1.60  and  its  two  surfaces  having  radii  of  minus  8  inches  and  plus 
4  inches. 

If  one  surface  of  the  lens  is  convex  and  the  other  surface 
concave,  the  focus  would  be  real  or  virtual  according  as  the  con- 
vex or  the  concave  curvature  was  the  greater. 

We  use  the  same  formula  as  in  the  previous  question: 

„  -8X4  -32  i:!^-u 

F  =  (-8  +4)  (1.60-1)  =    -  4  X  .60   =   "  '^'^  '"^^^^ 

This  would  mean  a  periscopic  concave  lens  and  the  focus 
would  be  a  negative  one. 


What  would  he  the  curvature  of  a  meniscus  lens  on  its  concave 
surface  if  the  convex  surface  had  a  curvature  of  5  inches,  its  focal 
distance  was  at  12  inches,  and  its  index  of  refraction  was  1.60? 

In  order  to  ascertain  the  radius  of  curvature  of  one  of  the 
surfaces,  when  that  of  the  other  and  the  index  of  refraction  and 


/ 


64  State  Board  Examinations 

the  focal  distance  are  known  we  can  make  use  of  the  same  formula, 
substituting  the  values  of  the  known  quantities  and  thus  find  the 
value  of  the  unknown  quantity, 

12   =    ^I 

(5  +  r)  (.60) 

or  5  r  =  12  (3  +  .6  r) 
or  5  r  =  36  +  7.2  r 
or  —  2.2  r  =  36 
or  r  =  —  16.36  inches 


What  is  the  dioptric  power  or  number  of  a  lens  whose  radii  of 
curvature  are  10  cm.  positive  and  40  cm.  negative,  and  the  ijidex  of 
refraction  1.54? 

In  this  case  the  formula  is 

^  _  100  (m  -  1)  (r  +  rO 
r  r' 

Substituting  figures 

n  =  (IQO   X   .54)   (10  +   (   -  40)  ) 
10  X    -  40 

54   X    -  30         -   1620 


D   = 


-  400  -  400 

D  =  +  4.05  D. 


Find  the  dioptric  number  of  power  of  a  lens  when  the  object 
is  placed  50  cm.  in  front  of  it  and  the  image  12.5  cm.  behind  it? 

50  cm.  represents  a  dioptric  power  of  2,  and  12.5  cm.  a 
dioptric  power  of  8,  and  the  sum  of  the  two  represents  the  dioptric 
power  of  the  whole  lens,  viz., 

8  +  2  =   10  D. 


Find  the  index  of  refraction  of  a  periscopic  lens  whose  focal 
distance  was  24  cm.,  and  its  radii  of  curvature  respectively  +  6  and 
—  12  cm.? 

lA              6  X  -  12      -,      -  72 
24  =  -7 .^,  , —    or  24  = 


(6  -  12)  ("  -  1)        -  6  M  +  6 
or  -  72  =  -  144  M  +  144  or  -  216  =  -  144  " 
or  144  M  =  216  or  /x  =  1.50. 


Theoretic  Optics  65 

The  index  of  refraction  in  this  case  is  1.50. 


A  parallel  beam  of  light  passes  through  a  convex  lens  of  2  D., 
which  is  three  inches  in  diameter;  ivhat  is  the  shape  and  size  of  the 
patch  of  light  it  casts  on  a  screen  ten  inches  away? 

This  being  a  spherical  lens  the  rays  of  light  will  be  equally 
refracted  in  all  meridians  and  will  be  brought  to  a  focal  point 
twenty  inches  from  the  lens.  As  it  leaves  the  lens  the  patch  of 
light  will  be  circular  in  shape  and  the  same  size  as  the  lens,  that 
is  three  inches  in  diameter,  and  gradually  lessens  until  it  is  con- 
tracted to  a  point  at  the  focal  distance.  At  a  distance  of  ten 
inches,  which  is  one-half  the  principal  focal  distance,  it  will  have 
lessened  one-half  and  form  a  circle  of  light  one  and  a  half  inches 
in  diameter.  

A  sphero-cylindrical  lens  -{-  5  D.  S.  =  —  1.50  D.  C.  axis  90° 
is  two  inches  in  diameter.  If  a  parallel  beam  of  light  passes  through 
this  lens,  what  is  the  shape  and  size  of  the  patch  of  light  it  casts  on  a 
screen  15  cm.  away? 

In  the  vertical  meridian  the  lens  will  have  the  full  power  of 
the  sphere  and  will  bring  parallel  rays  of  light  to  a  focus  at  a  dis- 
tance of  20  cm. 

In  the  horizontal  meridian  the  power  of  the  sphere  will  be 
reduced  by  the  concave  cylinder  to  +  3.50  D.,  thus  causing 
parallel  rays  of  light  to  meet  in  a  focus  at  a  distance  of  about 
29  cm. 

The  light  passing  through  the  vertical  meridian  conveying  to 
the  focal  point  20  cm.  away,  meets  the  screen  at  a  distance  of  15 
cm.,  and  as  this  is  ^  the  distance  from  the  lens,  the  patch  of  light 
will  be  lessened  in  the  same  proportion,  that  is  to  one-half  inch. 

The  light  passing  through  the  horizontal  meridian  converg- 
ing to  a  point  29  cm.  away,  meets  the  screen  at  15  cm.,  which  is 
15/29  of  the  focal  distance,  and  therefore  the  patch  of  light  will 
be  reduced  to  14/29  of  two  inches,  which  is  28/29  of  an  inch. 

The  patch  of  light  will  be  oval  in  shape,  measuring  one-half 
inch  vertically  and  28/29  of  an  inch  horizontally. 


//  an  object  be  held  100  cm.  in  front  of  a  —  5  D.  lens,  what  is 
the  character  and  location  of  the  image  formed? 


66  State  Board  Examinations 

This  is  a  problem  referring  to  conjugate  foci  of  concave 
lenses,  which  refract  light  with  that  degree  of  divergence  as  if  the 
rays  originated  from  the  principal  focal  distance  of  the  lens. 
In  the  case  of  the  —  5  D.  lens  in  the  question,  the  rays  would 
appear  to  diverge  from  a  distance  of  20  cm. 

If  the  object  is  nearer  than  infinity,  the  rays  from  it  striking 
the  lens  are  divergent,  but  this  divergence  would  be  increased 
by  the  concave  lens,  and  would  make  the  light  appear  to  originate 
from  a  point  closer  than  the  principal  focal  distance  of  the  lens. 

If  D.  represents  the  refractive  power  of  the  lens,  and  the 
distance  of  the  object  be  expressed  in  diopters  as  di  and  the 
distance  of  the  image  as  d2,  then  the  formula  is 

D.  =  di  +  do 

In  the  case  of  a  concave  lens  it  must  be  remembered  that 
the  D.  and  d2  are  negative,  and  the  formula  would  be 

D.   =  di  +  (-  d2) 
or  d2  =   D.    —  di. 

Substituting  the  figures  in  the  above  question  we  have 
d2=-5-l  =   -6D. 

And  if  do  represents  a  dioptric  power  of  —  6  D.,  then  the 
distance  is  100/'6  or  —  16.66  cm.,  which  means  a  virtual  image 
16.66  cm.  in  front  of  the  lens. 

If  rays  diverge  from  100  cm.  to  a—  5  D.  lens,  after  passing 
through  the  lens  they  are  divergent  as  if  they  came  from  16.66 
cm. 

What  is  the  general  formula  for  calculating  the  size  of  object 
or  image,  and  give  an  ilhistration  of  it? 

The  relative  sizes  of  object  and  image  are  proportional  to 
their  respective  distances  from  the  center  of  the  lens,  and  this 
statement  is  true  for  the  virtual  images  of  both  convex  and 
conjcave  lenses. 

When  the  object  is  at  twice  the  principal  focal  distance,  the 
size  of  the  image  is  the  same;  when  it  is  farther  away  than 
twice  the  focal  distance,  the  image  is  smaller;  when  the  object 
is  less  than  twice  the  focal  distance,  the  image  is  larger. 

Let  fi  represent  the  distance  of  the  object,  f2  the  distance  of 
the  image,  hi  the  size  of  the  object  and  h2  the  size  of  the  image, 
then  the  proportions  are 

fi  :   f2  ::   hi  :   ha 


Theoretic  Optics 


67 


from  which  we  get  the  following  formula: 


h2    = 


hi  U 


This  formula  is  applicable  in  all  cases  whether  the  image 
be  real  or  virtual,  and  whether  the  lens  be  convex  or  concave. 

For  instance,  if  the  size  of  the  object  be  1  inch  and  its 
distance  5  feet,  and  the  image  be  at  a  distance  of  5  inches,  then 

1  X  5    ^  _5.  ^  J_- 
60       ~  60  ~  12  '"• 


ho    = 


The  size  of  the  image  in  this  case  is  1/12  inch. 


Draw  a  diagram  showing  the  construction  of  a  real  image 
by  a  convex  lens. 

In  the  construction  of  the  image  of  an  object  formed  by  a 
convex  lens,  there  are  three  rays  which  must  be  considered  and 
followed  : 

1.  The  ray  which  passes  through  the  optical  center  (O  c), 
which  is  not  refracted, 

2.  The  ray  which  is  parallel  to  the  principal  axis  and  which 
after  refraction  passes  through  F2. 

3.  The  ray  which  passes  through  Fi,  and  which  after 
refraction  runs  parallel  to  the  principal  axis. 

The  second  and  third  rays  are  the  ones  necessary  to  be 
drawn  in  order  to  locate  the  image  of  a  point. 


A 

h 

\F2 

fl 

^^TfT---^ 

^ 

c     \ 

Bi 

~M 

H/^^--~^^ 

tr 

B 

A\ 

Fig.  10 

In  this  diagram  A  B  represents  the  object  and  B'  A'  the 
inverted  image. 

Draw  the  principal  axis  from  the  object  to  the  image  through 
the  optical  center. 

Draw  line  from  A  to  E  parallel  to  the  axis.  This  line  is 
then  refracted  and  passes  through  F^  extending  to  A'. 


68  State  Board  Examinations 

Draw  line  from  A  to  //  passing  through  Fi.  This  line  after 
refraction  is  parallel  to  the  axis  and  extends  to  A'. 

Draw  line  from  ^  to  ^'  passing  through  the  optical  center. 

The  three  lines  originating  from  A  meet  at  A' ,  and  therefore 
A'  is  the  image  of  A. 

In  the  same  way  B'  can  be  constructed  as  the  image  of  B, 
and  then  B'  A'  represents  the  position  and  size  of  the  real  inxerted 
image  of  the  object  A  B. 

If  an  object  be  placed  20  inches  in  front  of  a  6-inch  convex 
lens,  and  it  is  desired  to  form  the  image  at  10  inches,  ivhat  power 
of  lens  must  be  added? 

If  it  is  desired  to  move  the  image  from  i^  to  some  other 
position,  say  to  a  more  distant  position  expressed  as  X,  or  a 
nearer  position  expressed  as  y,  there  must  be  added  to  the 
origmal  lens  another  lens  whose  power  would  be  the  difference 
between 

■^  and   -j- 
or 

—  and  -T- 
y  '2 

For  instance,  if  i^  be  at  40  cm.  and  it  is  desired  to  move  it 
to  50  cm.,  which  is  represented  by  x,  then  fa  =  2.50  D.  and  X  = 
2  D.  and  the  difference  —  .50  D.,  the  necessary  lens  to  be  added 
is  concave  because  x  is  more  distant  than  fa. 

For  instance,  again,  if  fa  is  situated  at  40  cm.  and  it  is  desired 
to  bring  it  up  to  20  cm.,  which  is  represented  by  y,  then  fa  =  2.50 
D.  and  y  =  5  D.,  and  the  difference  between  the  two  is  +  2.50  D., 
the  necessary  lens  to  be  added  must  be  convex  because  y  is 
closer  than  fa. 

In  the  above  question,  in  order  to  find  the  position  of  fo, 
we  must  subtract  1/20  from  1/6  which  equals  7/60,  from  which 
we  must  subtract  1/10  (the  desired  distance  of  image  being  10 
inches)  and  the  result  is  1/60.  Therefore,  as  x  is  more  distant  than 
fa  the  necessary  lens  is  a  60-inch  concave  to  be  added  to  the  6-inch 
convex.  

Draw  a  diagram  showing  the  construction  of  an  image  by  a 
concave  lens. 


Theoretic  Optics 


69 


In  this  diagram  ^  5  is  an  object  in  front  of  a  concave  lens, 
the  principal  focus  of  which  is  at  F. 

From  A  we  draw  a  line  to  H,  passing  through  the  optical 
center  of  the  lens. 


Fig.  il 


Draw  another  line  from  yl  to  £  parallel  to  the  axis,  which 
after  refraction  is  diverged  as  if  it  came  from  F. 

These  two  lines  being  divergent  can  meet  only  when  produced 
backward  when  they  come  together  at  Ai,  which  is  the  image  of  ^. 

Similar  Hnes  from  B  meet  at  Bi,  which  is  the  image  of  B. 

Therefore,  Ax  Bx'xs  the  complete  image  of  the  object  A  B. 


How  is  the  magnifying  poiver  of  lenses  expressed? 

The  absolute  magnification  of  an  object  is  expressed  by  the 
ratio  between  the  angle  subtended  by  the  image  at  the  eye  and 
the  angle  subtended  by  the  object  at  the  eye. 

If  the  former  angle  is  represented  hy  A  I  and  the  latter  by 
A  0  then  the  magnification  is  expressed  as  follows: 

A  I 
A  0 

It  may  also  be  defined  as  the  ratio  between  the  size  of  the 
image  and  the  size  of  the  object  on  a  comparison  of  both  at  the 
same  distance  from  the  eye. 

The  apparent  magnification  is  the  size  of  the  object  in  com- 
parison with  that  of  the  image  at  its  point  of  most  distinct  vision. 

It  is  more  difficult  to  estimate  magnification  in  relation  to 
the  eye  than  when  the  image  is  thrown  upon  a  screen.  In  the 
latter  case  the  image  and  the  object  can  both  be  measured,  and 
the  first  divided  by  the  second  will  show  the  true  magnification. 

But  in  the  case  of  the  eye  we  are  unable  to  determine 
magnification  by  so  simple  a  method,  for  various  reasons.  The 
nearness  of  distinct  vision  varies  in  different  persons;  so  also 
does  the  size  of  the  retinal  image  vary  with  accommodation  and 


70 


State  Board  Examinations 


shape  of  the  eye,  and  also  the  distance  of  the  lens  from  the  eye 
and  from  the  object.  And  then  besides  there  is  a  mental  condi- 
tion which  affects  the  apparent  relative  size.  If  several  persons 
were  asked  the  size  of  the  moon  as  it  appears  to  them,  they  would 
probably  all  give  a  different  estimate. 


Fig.  12 

If  d  represents  the  distance  of  most  distinct  vision,  then 
the  usual  formula  to  express  the  magnifying  power  of  the  lens  is 

M    =  pi or  -=  +  1 

And  as  10  inches  is  allowed  for  the  distance  of  most  distinct 
vision,  for  the  average  eye,  we  can  substitute  this  figure  and  the 
formula  will  read 

M    =    l+f 

For  lenses  expressed  in  diopters,  it  would  be 

M    =    1+^ 

By  way  of  illustration,  if  we  use  a  5-inch  convex  lens, 

M     =    1    +^  =   3 

Such  5-inch  lens  is  equivalent  to  an  8  D.  lens,  with  which 

M  =  1  +  4-  =  3 

4 


Draw  a  diagram  showing  the  construction  of  a  virtual  image 
by  a  convex  lens. 


Theoretic  Optics 


71 


Draw  line  from  A  to  E  parallel  to  the  axis,  which  line  after 
refraction  will  pass  through  F2. 

Draw  another  line  from  A  passing  through  the  optical  center. 

These  two  lines  are  divergent  as  regards  each  other  and 
could  not  meet  to  form  a  real  image;  but  by  producing  them 
backwards  they  will  meet  at  ^\  which  is  the  virtual  image  of  A. 

Similar  lines  from  B  would  locate  its  virtual  image  at  Bi, 
and  hence  A^  Bi  is  the  complete  virtual  image  of  the  object  A  B. 


What  is  the  effect  produced  by  altering  the  position  of  a  convex 
lens,  and  give  several  illustrations? 

l3lN 


Fig.  13 
The  power  of  a  convex  lens  is  represented  by  p,  which  is 
the  reciprocal  of  its  principal  focal  distance.  If  the  latter  is 
10  inches,  the  power  is  1/10.  It  is  self-evident  that  the  power 
and  focal  distance  are  fixed  quantities,  but  at  the  same  time 
it  is  true  that  the  power  of  the  lens,  in  relation  to  a  given  point, 
varies  with  its  distance  from  that  point;  that  is,  when  a  convex 
lens  is  moved  away  from  a  given  plane,  it  acts  with  increased 
power  as  regards  that  plane,  or  in  other  words,  like  a  lens  of 
shorter  focus. 


72  State  Board  Examinations 

And  con\ersely,  a  convex  lens  loses  in  power  as  regards  a 
certain  plane  when  moved  closer  to  it,  or  in  other  words,  like  a 
lens  of  longer  focus. 

Referring  to  diagram  A  in  the  illustrations  below,  it  is  seen 
that  parallel  rays  of  light  entering  a  10-inch  convex  lens  are 
brought  to  a  focus  at  a  distance  of  10  inches  from  the  lens. 

If  a  40-inch  convex  lens  is  placed  in  contact  with  it  as  in 
diagram  B,  the  two  lenses  will  have  a  principal  focal  distance  of 

i^+^  =  ^°'i"'   ^■•^-  8  inches 

and  then  the  parallel  rays  will  be  brought  to  a  focus  at  a  distance 
of  8  inches.  The  same  result  will  be  obtained  if  the  10-inch  lens 
is  moved  farther  away,  as  in  diagram  C,  thus  proving  that  a 
con\ex  lens  acts  with  increased  powers  as  it  is  moved  farther 
awa>'. 

If  a  40-inch  concave  lens  is  placed  in  contact  with  the 
10-inch  con\ex  lens,  the  combined  lenses  will  have  a  principal 
focal  distance  of 

and  then  parallel  rays  will  be  focused  at  13  inches,  as  shown  n 
diagram  D. 

The  same  effect  is  produced  if  the  10-inch  convex  lens  is 
moved  closer,  as  in  diagram  E,  thus  proving  that  a  convex  lens 
acts  with  diminished  power  as  it  is  moved  closer. 

If  p  represents  the  power  of  a  convex  lens,  and  d  the  given 

distance  which  it  is  moved,  then  its  power  would  be 

1 
F    -    d  .     • 

Using  the  figures  in  diagrams  A,  B  and  C, 

1  1 


10-2         8 

The  shorter  distance  represents  a  stronger  lens. 

If  a  convex  lens  be  moved  to  a  greater  distance  than  its 
principal  focus,  not  only  will  its  converging  power  be  neutralized, 
but  it  will  have  the  effect  of  a  concave  lens.  If  this  10-inch 
convex  lens  be  moved  to  13  inches  from  a  screen,  the  rays  will 
meet  at  10  inches,  that  is  3  inches  in  front  of  the  screen,   and 


Theoretic  Optics 


73 


striking  the  screen  with  this  divergence  will  have  the  effect  of  a 
three-inch  concave  lens,  as  follows: 

1  1     .        ,  .    , 

Yj^ r-,   —    — ^;  t.  e.,  6  inches  negative 


What  is  the  effect  produced  by  altering  the  position  of  a  concave 
lens,  and  give  several  illustrations? 

When  a  concave  lens  is  moved  farther  away  from  a  point 
back  of  the  lens,  its  power  is  decreased  and  it  acts  as  a  lens  with 
a  longer  focus. 

If  a  concave  lens  is  moved  closer,  its  power  is  increased,  and 
it  acts  as  a  lens  with  a  shorter  focus. 

I31N.  I01N.8IN. 


c 

___---- 

r 

___ 

10 

iU 

G 

*rrr. 





■  —12 

H 

---■ 



-lOlN. 

J 

^  ^  —  —  —  "' 

f 

"~~~-— ---___ 

K 

__._------' 

'"~~ 

—  lOIN. 


Fig.  14 


When  parallel  rays  of  light  pass  through  a  10-inch  concave 
lens,  they  will  be  diverged  as  if  they  came  from  a  point  10 
inches  in  front  of  the  lens,  as  shown  in  diagram  F. 

If  a  13-inch  concave  lens  is  made  use  of,  the  negative  focus 
would  be  13  inches  in  front  of  the  lens,  as  shown  in  digram  G. 

But  the  same  effect  can  be  produced  by  moving  the  10-inch 
concave  lens  front  3  inches,  as  shown  in  diagram  H,  where  the 
effect  of  the  10-inch  lens  is  reduced  to  that  of  the  13-inch  lens. 


74  State  Board  Examinations 

thus  proving  that  the  power  of  a  concave  lens  is  decreased  by 
moving  it  away  from  a  given  point  back  of  the  lens. 

If  an  8-inch  concave  lens  be  used  the  negative  focus  will  be 
at  8  inches,  as  shown  in  diagram  /. 

But  the  same  effect  can  be  produced  by  moving  the  10-inch 
lens  back  2  inches,  as  shown  in  diagram  K,  where  the  effect  of 
the  10-inch  lens  is  increased  to  that  of  the  8-inch  lens,  thus 
proving  that  the  power  of  a  concave  lens  is  increased  by  moving 
it  closer  to  a  given  point  back  of  the  lens. 


What  is  the  effect  produced  hy  two  convex  lenses  when  they  are 
separated  from  each  other?    Give  an  example. 

The  combined  power  of  two  lenses  when  placed  close 
together  is  equal  to  the  sum  of  the  power  of  each,  just  as  simply  as 
2  +  2=4. 

But  if  the  two  lenses  are  not  in  actual  contact,  that  is,  if 
they  are  appreciably  separated,  the  resultant  effect  will  not  be 
the  same  as  when  they  are  together,  which  fact  is  easy  of  demon- 
stration by  a  drawing. 

Parallel  rays  of  light  striking  the  first  lens,  which  is  a  16- 
inch  convex  lens,  will  be  converged  so  as  to  meet  at  the  point  A, 
which  is  16  inches  behind  it. 

'  2 

F 


I6^   3 IN.    (ioT^- -.TT-A 


Fig.  15 

But  on  their  way  when  3  inches  from  the  first  lens,  they 
meet  the  second  lens,  which  is  a  10-inch  convex  lens,  and  if 
they  would  still  meet  at  the  point  A,  they  are  now  converging 
to  a  point  13  inches  (16  —  3)  behind  the  second  lens. 

Therefore,  the  power  of  the  first  lens  at  the  position  of  the 
second  lens,  is  increased  from  1/16  to  1/13,  which  means  that 
the  resultant  effect  will  be  the  same  as  if  a  13-inch  lens  was 
placed  in  contact  with  the  second  lens,  and  the  combined  power 
of  the  two  lenses  as  separated  will  be 

13  +  To  =  5:6  '"^^^^^  ^^  fa  +  fO  =   "6 

as  it  would  be  if  the  lenses  were  close  together. 


Theoretic  Optics  75 

If  Fi  represents  the  front  lens  and  F2  the  back  lens,  and  d 
the  distance  between  them,  and  F  the  focal  distance  of  the 
combination,  then  the  formula  for  finding  F  would  be 


Fi  — d    '   F2       F 
Substituting  the  figures  in  the  above  example: 


(16-3)    '    10        5.6 

The  distance  of  F  would  differ  considerably  if  these  lenses 
were  reversed  and  the  10-inch  lens  faced  the  light,  and  the  16- 
inch  lens  was  3  inches  behind  it.  When  so  arranged,  according 
to  the  formula  given  above,  the  result  would  be 

_L_  +1  =  1 

10  -  3  ^  16       4.8 


What  is  the  effect  of  two  concave  lenses  when  they  are  separated 
from  each  other?  Give  an  example. 

If  the  two  lenses  are  close  together  their  combined  power 
would  be  equal  to  the  sum  of  their  individual  powers,  as  for 
instance,  if  a  —  2  D.  lens  was  placed  against  a  —  3  D.  lens,  the 
combined  power  would  be  equal  to  —  5  D.  But  if  the  lenses  are 
separated  the  resultant  efifect  will  not  be  the  same. 


Parallel  rays  of  light  striking  the  first  lens,  which  is  a  20- 
inch  concave  lens,  will  be  diverged  as  if  they  came  from  a  point 
20  inches  in  front  of  the  lens. 

After  traveling  4  inches  the  rays  meet  the  second  lens,  which 
is  24  inches  from  the  negative  focus  of  the  first.  Therefore,  we 
have  a  divergence  of  1/24  added  to  a  divergence  of  1/10  (which 
represents  the  negative  power  of  the  second  lens,  a  10-inch  con- 
cave), which  equals  a  total  divergence  of  1/7. 

Using  the  formula  previously  given: 

-L_  +_L  =_i 
-  20-^  ^  -  10         7 


76  Stale  Board  Examinations 

If  an  object  be  placed  40  ijtches  in  front  of  a  16-i}jch  lens 
convex,  and  4  inches  behind  which  a  26-inch  concave  lens  is  placed, 
where  will  the  image  be  formed? 

When  light,  falHng  upon  a  lens,  is  divergent  instead  of 
parallel,  the  conjugate  focus  must  be  found  before  we  can  make 
use  of  our  formula. 

In  this  case,  where  rays  diverge  from  a  point  40  inches  in 
front  of  the  lens,  which  is  a  16-inch  convex,  the  conjugate  focus 
would  be  ^ 


1 
16 

- 

1 
40  ^ 

3 
"  80' 

1 
or^-y 

at  is  at 

27: 

inches. 

Then 

we 

have 

27" 

1 
-  -i 

+ 

(- 

1 
26 

)  = 

1 
199 

Therefore,  the  image 

is 

at  199  inches 

What  is  the  effect  of  a  convex  arid  a  concave  lens  ivhen  separated? 
Give  several  examples. 

When  a  convex  and  a  concave  lens  of  equal  power  are  placed 
in  contact,  there  is  neutralization  and  parallel  rays  would  pass 
unrefracted,  but  if  the  lenses  are  separated,  one  or  the  other  will 
predominate,  as  the  case  may  be. 

If  the  distance  between  the  lenses  is  less  than  the  focal  length 
of  the  first  or  convex  lens,  the  combination  will  be  a  positive  one; 
if  the  distance  between  the  lenses  exceeds  the  focal  distance  of 
the  first  lens,  then  the  combination  will  be  negative. 

2 


Parallel  rays  of  light  striking  the  first  lens,  which  is  an  8-inch 
convex,  will  be  converged  so  as  to  meet  in  focus  at  a  point  8 
inches  away.  But  after  having  traveled  4  inches,  they  meet  the 
concave  lens  of  8  inches,  and  at  that  point  they  have  a  conver- 
gence of    -f  X.  which  is  partly  overcome  by  the  1/8  divergence  of 


Theoretic  Optics  11 

the  concave  lens,  causing  the  rays  to  meet  at  a  point  8  inches 
back  of  the  second  lens. 

Using  the  proper  formula 


.-(-f) 


1        ,   /         1    \  i_ 

^    8 


which  means  a  positive  focus  at  8  inches. 

If,  instead  of  a  convex  and  concave  lenses  being  of  equal 
focal  length,  the  concave  be  the  shorter,  and  then  when  placed  in 
contact,  the  concave  lens  will  predominate  and  no  real  image 
can  be  formed. 

If  now,  the  convex  lens  be  mo\ed  forward  towards  the 
light,  it  will  increase  in  power  until  the  point  is  reached  where 
the  separation  is  equal  to  the  sum  of  their  focal  lengths,  and  then 
neutralization  will  occur  and  the  rays  will  issue  parallel. 

If  the  convex  lens  is  moved  still  closer  to  the  light,  it  pre- 
dominates, increasing  until  the  separation  equals  the  focal  dis- 
tance of  the  convex  lens,  when  it  is  at  its  maximum. 

In  the  separation  of  a  convex  and  a  concave  lens,  the  result 
will  be  different  as  the  light  strikes  first  the  convex  or  the  concave. 

In  the  above  illustration,  where  an  8-inch  convex  lens  was 
4  inches  in  front  of  an  8-inch  concave  lens,  we  found  that  F  was 
at  8  inches. 

But  if  the  first  lens  was  the  concave  one,  then  the  result 
would  be 


-  8  -  4   '     8  '24 

that  is  F  would  be  at  24  inches.  And  from  this  we  learn  that  F 
is  closer  when  the  convex  lens  is  nearer  the  light,  and  farther 
away  when  the  concave  lens  is  nearest  the  light. 


//  an  object  he  placed  80  inches  in  front  of  a  14-inch  convex 
lens,  where  must  a  10-inch  concave  lens  be  placed  so  as  to  render 
the  rays  parallel? 

When  the  rays  of  light  instead  of  being  parallel  are  diver- 
gent when  they  enter  the  lens,  as  in  this  case,  we  must  find  the 
conjugate  focus  before  the  value  of  d  (representing  the  distance 
between  the  lenses)  can  be  applied  to  the  front  lens  of  the  com- 
bination. 


78  State  Board  Examinations 

It  will  be  remembered  that  the  formula  for  conjugate  foci 
was 

J-   _  i  =  J- 

F       .  fi   ~    tj 

Substituting  the  figures  in  this  question  we  have 

J_  _  J_  =  _^      J_ 
14       80  ~  1120°'' 17 

The  image  is  17  inches  back  of  the  14-inch  convex  lens. 

And  in  order  to  find  where  the  10-inch  concave  lens  must  be 
placed  to  secure  parallelism,  we  have 

17  —  10  =  7  inches, 
it  must  be  placed  7  inches  back  of  the  convex  lens. 

When  the  light  leaves  the  convex  lens  the  rays  are  converg- 
ing to  a  point  17  inches  away;  but  at  a  distance  of  7  inches  from 
the  lens  they  are  converging  to  a  point  10  inches  away,  and  at 
this  position  a  concave  lens  of  10  inches  would  render  the  rays 
parallel.  Or  in  other  words,  the  convergence  to  10  inches  of  the 
convex  lens  would  be  neutralized  by  a  divergence  of  10  inches  of 
the  concave  lens. 


What  must  be  the  distance  between  a  10-inch  convex  lens  and  a 
4-inch  concave  lens,  in  order  to  produce  the  effect  of  a  40-inch 
convex  lens? 

It  will  be  remembered  that  the  formula  in  such  a  case  is 

^    (Fi  -  d)  F2 
Fi  -f  F2  -  d 

When  we  come  to  substitute  the  figures  in  the  question,  we  find 
we  have  figures  for  all  the  quantities  except  the  distance;  hence, 
we  must  WTite  it  as  follows: 

(10  -  d)    -  4 


-f  40   = 


or  +  40  = 


10  -  4  -  d 
-  40  +  4  d 


For  those  who  are  not  thoroughly  familiar  with  algebra  we 
would  say  that  when  we  multiply  +  10  by  —  4  the  result  is  —  40, 
and  when  we  multiply  —  d  by  —  4  the  result  is  +  4  d,  which  gives 
the  new  numerator. 


Theoretic  Optics  79 

And  for  the  denominator  we  add  +  10  and  —  4  and  the  result 
is  +  6.  It  might  be  remarked  here  that  when  no  sign  is  placed  in 
front  of  a  number,  it  is  understood  to  be  a  plus. 

Now,  in  order  to  get  rid  of  the  fraction  we  must  multiply  the 
above  equation  by  6  —  d,  and  the  result  will  be 
240  -  40  d  =   -  40  +  4  d 
Now,  we  must  get  the  d's  on  one  side  of  the  equation  and  the 
numbers  on  the  other  side,  and  then  we  have 
-  44  d  =   -  280 
d  =  6fT 
When  a  plus  number  is  carried  to  the  other  side  of  the  equation 
it  becomes  a  minus,  and  when  a  minus  number  is  carried  over  it 
becomes  a  plus. 

Now,  in  order  to  verify  the  result  we  can  use  the  formula  again 
as  follows: 

(10  -  6yV)    -  4 


+  10   -  4   -  6i\ 

3iV   X   (    -  4)    _    - 


=  40 


X-  =  40 

~    TT  ~    TT 

Therefore,  the  distance  between  the  10-inch  convex  lens  and 
the  4-inch  concave  lens  must  be  6tt  inches  in  order  to  produce 
the  effect  of  a  forty-inch  convex  lens. 


A  point  of  light  is  situated  two  meters  from  a  -{-  2  D.  spherical 
lens;  at  what  distance  will  the  image  he  formed? 

If  the  lens  is  the  same  number  concave,  where  and  what  will 
be  the  image?  The  rays  proceeding  from  the  light  at  a  distance  of 
two  meters  would  enter  the  lens  with  a  divergence  of  .50  D.  and, 
therefore,  the  lens  would  be  reduced  by  that  much  to  make  the 
rays  parallel.  In  other  words,  inasmuch  as  .50  D.  of  the  power  of 
the  lens  is  used  up  to  take  care  of  the  entering  rays,  there  would 
be  only  1.50  D.  left  to  act  on  the  emerging  rays,  which  would  bring 
the  light  to  a  focus  at  two-thirds  of  a  meter  on  the  opposite  side 
of  the  lens  from  the  light. 

If  these  rays  with  a  divergence  of  .50  D.  enter  a  concave  lens, 
their  divergence  would  be  increased  by  the  amount  of  divergent 
power  of  the  lens,  and  in  this  case  the  rays  would  emerge  from 
this  lens  with  a  divergence  of  2.50  D.,  which  would  indicate  a 


80  State  Board  Examinations 

negative  focus  of  two-fifths  of  a  meter  on  the  same  side  of  the 
lens  as  the  Hght. 

A  -\-  3  D.  spherical  lens  forms  an  image  of  a  light  at  a  distance 
of  50  cm.  on  the  opposite  side  of  the  lens  from  the  object;  at  what 
distance  is  the  light  from  the  image? 

If  the  image  was  at  a  distance  of  50  cm.  from  the  lens  on  the 
same  side  as  the  light,  what  would  be  the  distance  between  the 
object  and  the  image? 

A  +  3  D.  lens  would  bring  parallel  rays  to  a  focus  at  3?)  cm., 
but  if  the  image  is  formed  at  a  distance  of  50  cm.  it  must  be  that 
the  rays  that  enter  the  lens  are  divergent  instead  of  parallel,  and 
the  amount  of  divergence  would  be  represented  by  the  difference 
between  3  D.  and  2  D.,  this  latter  corresponding  to  the  diver- 
gence of  the  rays  from  the  image  at  a  distance  of  50  cm.  The  result 
is  1  D.,  which  means  a  distance  of  100  cm.  as  the  location  of  the 
light  from  the  lens;  or  a  distance  of  150  cm.  from  object  to  image. 

If  the  image  was  at  a  distance  of  50  cm.  from  the  lens  on  the 
same  side  as  the  light,  this  would  mean  the  virtual  image  of  a 
convex  lens,  due  to  the  fact  that  the  object  was  closer  to  the  lens 
than  its  principal  focal  distance. 

This  negati\'e  focal  distance  of  50  cm.  indicates  a  divergence 
of  2  D.  and  if  this  amount  remained  after  passing  through  a  -f  3 
D.,  the  original  divergence  must  have  been  5  D.,  corresponding 
to  a  distance  of  20  cm.  as  the  position  of  the  object. 

And  if  the  distance  of  the  object  is  20  cm.  and  of  the  image  50 
cm.  on  the  same  side  of  the  lens,  the  distance  between  object  and 
image  must  be  30  cm. 

An  image  of  a  distant  point  of  light  is  formed  on  a  screen  by 
means  of  a  convex  spherical  lens.  If  the  lens  is  tilted  so  that  it  is 
inclined  at  an  angle  of  45  degrees  to  the  direction  of  the  incident 
rays,  there  are  two  positions  of  the  screen,  as  it  is  moved  closer  to 
and  farther  from  the  light,  in  which  the  ijnage  takes  the  form  of  a 
luminous  straight  line  at  right  angles  to  each  other  in  the  tivo  posi- 
tions.    What  is  the  explanation? 

When  a  spherical  lens  is  held  obliquely  to  incident  rays  of 
light,  and  added  cylindrical  effect  is  produced,  and  it  acts  as  a 


Theoretic  Optics  81 

sphero-cylindrical  lens.  If  the  spherical  lens  be  held  at  its  focal 
distance  from  the  screen  and  parallel  to  it,  a  perfect  image  of  a 
distant  point  of  light  is  formed  upon  the  screen ;  but  if  the  lens  be 
held  obliquely  the  image  is  distorted  and  elongated  as  if  a  cylinder 
had  been  added  to  the  sphere.  Two  bright  focal  lines  are  formed 
on  the  screen  at  right  angles  to  each  other  when  the  lens  is  held 
at  the  proper  distance  for  each. 

The  obliquity  of  the  lens  increases  the  refractive  power  of 
both  meridians,  but  more  decidedly  so  in  the  meridian  at  right 
angles  to  the  axis  of  rotation.  Therefore,  the  efTect  produced  is 
that  of  a  slightly  stronger  sphere  combined  with  a  cylinder  whose 
axis  would  correspond  to  the  axis  of  rotation.  In  like  manner 
rotation  of  a  cylindrical  lens  around  its  axis  causes  increased  effect 
in  the  meridian  at  right  angles  thereto. 

If  a  convex  sphere  be  held  upright  and  parallel  to  a  screen, 
it  will  form  a  circular  image  of  a  point  of  light  that  is  on  a  level 
with  the  axis  of  the  lens;  but  if  the  lens  be  tilted  around  a  hori- 
zontal axis,  it  will  no  longer  form  a  circular  image,  but  will  pro- 
duce two  ill-defined  lines,  one  vertical  a  little  closer  than  the 
original  focus,  and  another  horizontal  much  nearer  the  lens;  the 
latter  as  a  result  of  the  increase  of  power  in  the  meridian  of  rota- 
tion. This  increase  of  power  is  due  to  the  fact  that  the  light  passes 
through  a  greater  thickness  of  glass  when  the  lens  is  oblique  than 
when  it  is  in  its  proper  position. 

If  a  -f  1  D.  sphere  be  rotated  45°,  the  approximate  effect 
produced  would  be 

+  1.20  D.  S.  C  +  1.20  D.  cyl. 
which  would  show  a  focal  line  in  one  meridian  at  83  cm.  and  in 
the  other  meridian  at  42  cm. 


An  object  is  held  80  inches  in  front  of  two  lenses,  the  first  of 
which  is  a  14-inch  convex  and  the  second  is  a  10-inch  concave. 
It  is  desired  to  focus  the  image  40  inches  behind  the  concave  lens; 
what  must  be  the  distance  between  the  two  lenses  to  accomplish 
this? 

As  the  object  is  only  80  inches  in  front  of  the  convex  lens, 
the  rays  will  enter  it  divergently  and  the  image  will  be  formed 
not  at  the  principal  focal  distance  of  the  lens  (which  is  the  focus 
for  parallel  rays),  but  at  some  farther  distance.     This  distance 


82  State  Board  Examinations 

can  be  found  by  the  formula  for  conjugate  foci,  as  follows: 

11         66         ^        1 
14-80=  TT20°''"^°"'  17 

Therefore,  the  power  of  the  lens  has  been  reduced  to  that  of  a 
17-inch  convex  lens. 

Making  use  of  the  formula  for  the  effectivity  of  two  lenses 
when  separated,  and  substituting  the  above  figures  we  have 

40  =       (^7   -  d)    -   10 
17  +  (-   10)   -  d 

For  the  numerator  we  multiply  17   —  d  by  —   10,  and  for 
the  denominator  we  collect  and  simplify.    The  result  is 

-   170  +  lOd 
7   -  d 

In  order  to  get  rid  of  fractions  we  multiply  by  7  —  d,  and 
then  the  equation  will  read 

280  -  40  d  =  -  170  +  lOd 
Collect  the  d's  on  one  side  and  the  numbers  on  the  other: 
-  50  d  =   -  450 
d  =  9 
In  order  to  produce  the  desired  result  the  interval  between 
the  convex  and  the  concave  lens  must  be  9  inches. 


An  object  is  placed  60  inches  in  front  of  two  convex  lenses,  the 
first  of  which  is  a  30-inch  lens  and  the  second  is  a  40-inch  lens; 
what  must  he  the  distance  betiveen  the  two  lenses  in  order  that  the 
image  shall  he  formed  10  inches  behind  the  second  lens? 

As  the  rays  strike  and  enter  the  first  convex  lens  with  a 
divergence  of  Veo,  the  power  of  the  lens  is  practically  reduced  by 
that  much,  as  follows: 

JL  _  J_  =  J_ 
30         60  ~  60 

We  now  have  a  60-inch  convex  lens  and  a  40-inch  convex 
lens,  and  by  making  use  of  the  formula  given  in  the  previous 
question  we  have 

10  =  in"  r.rf^   ^!!  or  1000—10  d  =  2400— 40  d 

60-^-40   —  d 

30  d  =  1400 
2400    -    40d  ^      A^  r.  i-j 

"'^  ^Q  =      100   -  d  d  =  46  2/3 


Theoretic  Optics  83 

These  two  convex  lenses  must  be  separated  by  a  distance  of 
46%  inches  to  accompHsh  the  result  desired. 


What  does  a  compound  microscope  consist  of?  Give  a  brief 
description  of  it. 

The  compound  microscope  is  used  to  obtain  a  magnified 
view  of  small  objects  close  at  hand.  It  consists  of  two  convex 
lenses  which  are  separated  from  each  other,  the  amount  of 
separation  being  dependent  upon  the  length  of  the  instrument. 

The  first  lens  is  called  the  objective;  it  should  be  corrected 
for  aberrations,  and  forms  a  real  magnified  and  inverted  image 
of  an  object,  which  should  be  placed  just  beyond  its  principal 
focal  distance. 

The  second  lens  is  called  the  eye  lens,  or  eyepiece,  or  ocular; 
not  quite  so  strong  as  the  first,  by  the  aid  of  which  the  image  is 
viewed. 

If  S.  O.  represents  size  of  object,  D.  O.  its  distance  from  the 
microscope  and  D.  I.  the  distance  of  the  image  from  the  objective, 
then  the  size  of  the  image  will  be  equal  to 

P.   I.    X   S.  O. 
D.  O. 

The  magnification  can  be  increased  by  a  greater  separation 
between  the  two  lenses,  which  would  increase  D.  I.  Also  by 
bringing  the  object  closer  to  the  microscope,  which  would  decrease 
D.  O. 

If  the  image  formed  by  the  objective  is  located  at  the 
principal  focal  distance  of  the  eyepiece,  the  rays  would  be 
parallel,  the  object  would  seem  to  be  at  infinity  and  there  would 
be  no  strain  on  the  eye  of  the  observer. 

The  small  object  just  beyond  the  focal  distance  of  the 
objective  lens,  forms  a  real  image  of  the  object,  which  image 
is  inverted  and  magnified.  When  the  eye  of  the  observer  is 
behind  the  eyepiece,  there  is  seen  at  the  distance  of  most  distinct 
vision  a  more  magnified  image  of  the  object,  which  is  still  inverted 
and  is  now  virtual  instead  of  real  as  formed  by  the  objective. 


What  does  an  opera  glass  consist  of  ?     Give  a  brief  description 
of  it. 


84  State  Board  Examinations 

An  opera  glass  consists  of  a  convex  lens  and  a  concave  lens 
of  higher  power.  When  the  convex  lens  is  placed  in  front  of  the 
conca\e  lens  at  a  distance  that  is  equal  to  the  algebraic  sum  of 
their  focal  lengths,  the  lenses  neutralize  each  other  by  their 
separation.  If  Fi  represents  the  focal  length  of  the  first  or  convex 
lens,  and  F2  the  focal  length  of  the  second  or  concave  lens,  then 
the  amount  of  separation  is  equal  to  Fi  plus  F2,  and  this  is  the 
way  the  glasses  should  be  separated  for  an  emmetrope. 

In  the  case  of  hypermetropia  where  the  light  should  enter 
the  eye  in  convergent  rays  in  order  to  focus  on  the  retina,  the 
separation  of  the  lenses  should  be  a  little  greater;  while  in 
myopia  where  the  light  should  enter  the  eye  in  divergent  rays, 
in  order  that  vision  may  be  clear,  the  distance  between  the  lenses 
should  be  less. 

Although  the  rays  of  each  pencil  emerge  parallel  or  divergent 
from  a  very  distant  point  after  refraction  by  the  two  lenses,  yet 
the  pencils  themselves  are  deviated  so  that  the  object  appears 
under  a  larger  angle. 

The  magnification  produced  by  an  opera  glass  can  be 
expressed  by  the  fraction 

El 
F2 

If  the  focal  length  of  the  first  convex  lens  was  5  inches  and 
if  the  second  concave  lens  was  2  inches,  the  magnifying  power  is 

If  the  position  of  the  lenses  was  reversed  and  the  concave 
lens  was  placed  in  front,  then  the  object  viewed  would  appear 
diminished  in  size  in  the  same  ratio,  which  in  this  case  would  be 

5 
that  is  the  minification  would  be  2W  times. 


What  does  a  stereoscope  consist  of?  Give  a  brief  description 
of  it. 

The  stereoscope  is  a  box  or  frame  fitted  at  one  end  with  two 
sphero-prisms  bases  out  (which  are  really  the  transposed  halves 
of  one  large  convex  lens),  and  at  the  other  end  there  is  a  slide  that 
carries  two  photographs. 


Theoretic  Optics  85 

These  photographs  are  taken  from  slightly  different  stand- 
points, usually  about  2}i  inches  apart,  which  correspond  to 
the  average  pupillary  distance,  but  which  may  be  varied  for  the 
degree  of  stereoscopic  effect  desired. 

On  a  casual  glance  the  photographs  look  alike,  but  they  are 
really  dissimilar,  the  right  one  corresponding  to  the  image 
formed  in  the  right  eye  and  the  left  one  to  the  image  formed  in 
the  left  eye. 

As  the  action  of  a  prism  is  to  cause  an  apparent  displace- 
ment in  the  direction  of  its  apex,  the  lenses  of  the  stereoscope 
cause  the  apparent  position  of  each  photograph  to  be  displaced 
inwards  with  the  result  of  fusing  the  two  into  one,  and  that  with- 
out any  muscular  effort  on  the  part  of  the  eyes.  The  single  image 
that  is  produced  is  virtual  and  located  near  the  point  of  most 
distinct  vision  of  the  observer. 

This  instrument  artificially  produces  the  appearance  of 
solidity  and  perspective  that  naturally  results  from  binocular 
vision.  This  effect  is  given  to  flat  pictures,  because  each  eye 
obtains  a  view  identical  with  what  they  would  receive  when 
viewing  the  objects  directly. 

The  distance  between  the  prisms  and  the  photographs  is 
equal  to  the  focal  distance  of  the  spherical  lenses,  and  therefore 
an  emmetrope  will  need  to  use  neither  accommodation  or  con- 
vergence. If  hypermetropia  or  myopia  is  present,  the  distance 
will  have  to  be  altered  accordingly. 


What  does  a  telescope  consist  of?    Give  a  brief  description  of  it. 

The  telescope  is  used  to  obtain  an  enlarged  view  of  distant 
objects,  and  in  its  simplest  form  consists  of  two  convex  lenses, 
the  weakest  of  which  is  called  the  object  glass  or  objective,  and 
is  turned  toward  the  distant  object  that  is  to  be  viewed;  while 
the  stronger  is  called  the  eyepiece  or  eye  lens  and  it  is  placed 
immediately  in  front  of  the  eye.  Both  of  these  lenses  should  be 
corrected  for  spherical  and  chromatic  aberration. 

A  real  inverted  image  of  a  distant  object  is  formed  by  the 
objective,  and  this  image  as  seen  through  the  eyepiece  is  a  virtual 
one,  subtending  an  angle  greater  than  that  of  the  object,  and  it 
is  upon  the  ratio  between  these  two  angles  that  the  magnification 
depends. 


86  State  Board  Examinations 

Since  the  object  looked  at  is  a  distant  one,  the  rays  proceed- 
ing from  it  are  parallel,  and  hence  the  image  formed  by  the 
objective  will  be  at  its  principal  focal  distance.  If  it  is  desired 
that  in  an  emmetrope  the  image  be  seen  by  the  eye  without 
accommodation,  its  location  must  coincide  with  the  principal 
focal  distance  of  the  eyepiece. 

In  other  words,  the  parallel  rays  are  converged  by  the 
objective  to  a  focus  from  which  they  diverge  to  the  eyepiece, 
which  parallels  them,  so  that  they  can  be  focused  in  the  em- 
metropic eye  without  accommodation.  Therefore,  the  distance 
between  the  lenses  must  be  equal  to  their  focal  lengths. 

The  magnification  produced  by  a  telescope  when  adjusted 

to  suit  an  emmetropic  eye  without  accommodation  is  equal  to 

p 

p^    where  Fi  represents  the  focus  of  the  objective  and   F2  the 

focus  of  the  eye  lens. 

In  the  case  of  a  hypermetrope  the  telescope  would  be 
adjusted  so  that  the  distance  between  the  two  lenses  would  be 
greater  than  their  focal  lengths,  under  which  circumstances  the 
rays  would  enter  the  eyepiece  diverging  from  a  point  greater 
than  its  focal  distance,  and  hence  would  leave  the  lens  and  enter 
the  hypermetropic  eye  as  convergent  rays  and  thus  be  focused 
on  its  retina. 

In  the  case  of  a  myope,  the  telescope  would  be  adjusted  so 
as  to  lessen  the  distance  between  the  lenses,  and  then  the  rays 
would  enter  the  eyepiece  diverging  from  a  point  closer  than  its 
focal  distance,  and  hence  would  leave  the  rays  and  as  such 
would  be  focused  on  its  retina. 

To  obtain  high  magnification,  the  focal  distance  of  the 
objective  must  be  as  great,  and  of  the  eyepiece  as  short,  as 
possible;  for  this  reason  in  a  telescope  the  objective  must  be  a 
lens  of  long  focus  and  the  eyepiece  a  lens  of  short  focus. 

The  image  as  seen  by  the  eye  is  inverted,  but  with  respect 
to  heavenly  bodies  this  is  a  matter  of  no  importance.  If  so 
desired,  this  inversion  can  be  overcome  by  means  of  an  erecting 
eyepiece,  which  causes  a  reinversion  of  the  image,  the  objection 
to  which,  however,  is  that  there  is  a  loss  of  light  owing  to  the 
increase  of  the  refracting  surfaces. 


How  can  you  determine  the  position  and  magnitude  of  an 
image  of  an  object  placed  in  front  of  a  convex  lens?    An  arrow  5 


Theoretic  Optics  87 

inches  long  is  placed  8  inches  away  from  a  convex  lens  whose  focal 
length  is  3  inches.    Find  the  position  and  length  of  the  image. 

First  we  must  find  the  position  of  the  image.  As  the  arrow 
is  at  a  distance  of  8  inches,  the  rays  proceeding  from  it  would 
enter  the  convex  lens  of  3  inches  focal  length,  with  a  divergence 
of  1/8.  After  this  divergence  is  overcome  there  would  remain 
in  the  lens  a  convergence  power  of  ^p^,  which  is  found  as  follows: 

i    _    1   =    1   =  J_ 
3  8         24   ~   4  % 

Therefore,  the  position  of  the  image  would  be  4  4/5  inches 
from  the  lens.  In  order  to  find  the  length  of  the  image  we  have 
this  proportion;  the  distance  of  the  object  is  to  the  size  of  the 
object  as  the  distance  of  the  image  is  to  the  size  of  the  image. 

Substituting  figures  we  have 

8  :5  ::4y5  :X 

Y    _     5X4%     _    24  , 

^    -  8        ■    -    X    -^ 

Therefore,  the  length  of  the  image  is  3  inches. 


An  incandescent  gas  light,  with  a  mantle  10  centimeters  high, 
stands  at  the  same  level  as  a  converging  lens,  the  power  of  which  is 
5  D.,  situated  6  meters  to  the  right  of  the  light.  Find  the  position 
and  the  size  of  the  image  of  the  mantle.  If  the  light  is  then  lifted  up 
1  meter  above  its  former  position,  what  change  will  take  place  in 
the  position  of  the  image? 

Ordinarily,  in  the  practice  of  optometry,  we  make  our  tests 
of  the  acuteness  of  vision  at  a  distance  of  6  meters,  on  the  as- 
sumption that  rays  proceeding  from  this  distance  are  practically 
parallel.  But,  as  a  matter  of  fact,  these  rays  have  a  slight 
divergence. 

Six  meters  equal  600  centimeters,  and  the  amount  of  diver- 
gence would  be  found  by  dividing  600  into  100,  which  would  be 
0.17  D.  This  would  reduce  the  power  of  the  plus  5  D.  lens  to 
plus  4.83  D. 

The  focal  distance  is  found  by  dividing  4.83  into  100,  and 
the  result  is  20.7  centimeters,  which  would  be  the  position  of  the 
image. 


88  State  Board  Examinations 

The  length  of  the  image  is  found  by  using  the  proportion 
as  in  the  previous  question: 

600  cm.  :  10  cm.  ::  20.7  cm.  :  X 

_   10  cm.    X   20.7  cm. 
600  cm. 

207   cm.         r\-2Ac 
600   cm. 

The  length  of  the  image  is  0.345  cm. 

As  the  light  is  elevated  the  image  would  be  correspondingly 
depressed.  If  the  light  is  lifted  one  meter,  which  is  one-sixth  the 
distance  of  the  object,  the  image  would  be  lowered  in  the  same 
proportion,  that  is,  one-sixth  the  distance  of  the  image  (1/6  of 
20.7  cm.),  which  is  3.4  cm. 


//  the  refractive  index  from  air  to  glass  is  3/2,  and  that  from 
air  to  water  is  4/3,  what  is  the  ratio  of  the  focal  lengths  of  a  glass 
lens  in  water  and  in  air? 

This  is  equivalent  to  saying  that  when  light  passes  from  air 
into  glass  it  is  subject  to  an  index  of  refraction  of  1.50,  and 
when  it  passes  from  air  into  water  it  is  subject  to  an  index  of 
1.33,  but  when  it  passes  from  water  into  glass  the  conditions  are 
different. 

The  index  of  refraction  from  one  medium  to  another  is 
equal  to  the  refractive  index  of  the  latter  divided  by  that  of  the 
former.  For  all  practical  purposes  we  assume  air  to  be  the  unit, 
and  if  the  index  of  refraction  from  vacuum  to  glass  is  1.52,  or 
as  we  ordinarily  say,  the  index  of  refraction  of  glass  is  1.52, 
then  the  index  of  refraction  from  air  to  glass  is  1.52/1,  or  1.52. 

The  relative  index  of  refraction  is  the  expression  of  the 
refractivity  when  light  passes  from  one  dense  medium  into 
another  dense  medium,  as  from  water  into  glass  or  glass  into 
water.  According  to  the  rule  mentioned  above,  this  relative 
index  is  found  by  dividing  the  index  of  the  medium  into  which 
the  light  passes,  by  the  index  of  the  medium  from  which  it 
proceeds. 

In  this  question  where  the  light  passes  into  glass  with  an 
index  of  3/2  or  1.50  from  water,  with  an  index  4/3  or  1.33,  the 


Theoretic  Optics  89 

relative  index  is  found  by  dividing  3/2  by  4/3,  and  the  result  is 
9/8  or  1.125. 

Therefore,  as  the  refractive  index  from  air  to  glass  is  3/2 
or  1.50,  and  from  water  to  glass  is  9/8  or  1.125,  the  refractive 
index  of  the  glass  lens  in  water  is  reduced  from  1.50  to  1.125, 
the  latter  being  one-fourth  of  the  former;  then  the  focal  length 
of  the  lens  in  water  would  be  four  times  its  length  in  air. 


A  convex  and  a  concave  lens,  each  10  inches  in  focal  length, 
are  held  co-axially  at  a  distance  of  3  inches  apart.  Find  the  position 
of  the  image  if  the  object  is  at  a  distance  of  15  inches  beyond  the 
convex  lens,  and  also  the  position  if  the  lenses  were  reversed  and  the 
concave  lens  was  first. 

If  the  object  was  at  infinity  the  focal  distance  of  the  convex 
lens  would  be  at  10  inches,  but  inasmuch  as  the  rays  enter  the 
lens  cmergently  from  a  point  15  inches  away,  the  focus  of  the 
lens  would  be 

— -  —   —   =  :,-  or  at  30  inches. 
10        1:)        30 

The    formula    is:      p   _   ^   ~^  F^  "^   F 

Substituting  figures 

11         1         1         17         1 


30  -  3    '  10        27        10        270        16 

or  16  inches  from  the  concave  lens. 

There  would  be  considerable  difference  in  the  result  if  the 
concave  lens  was  in  front,  as  follows: 

If  parallel  rays  entered  the  10-inch  concave  lens,  its  negative 
focus  would  be  10  inches;  but,  inasmuch  as  the  rays  entered  the 
lens  with  a  divergence  of  Vio  the  effective  focus  of  the  concave 
lens  would  be 


1       1 

10        15 

5    _  J_ 
3U          0 

Using  the  formula  we  have 

-  6  -  3  ^   10 

•)    ^  10 

1 

"  90 

or  90  inches  from  the  concave  lens. 

90  State  Board  Examinations 

What  is  meant  by  the  focal  length  of  a  spherical  reflecting 
surface?  How  far  from  a  concave  mirror  of  radius  3  feet  would  you 
place  an  object  to  give  an  image  magnified  three  times?  Would  the 
image  be  real  or  virtual? 

Parallel  rays  striking  a  concave  mirror  are  reflected  in  such 
a  way  as  to  converge  to  a  point  on  the  axis  of  the  mirror,  which 
is  called  the  principal  focus  of  the  mirror. 

If  the  mirror  be  convex  the  rays  are  reflected  in  such  a 
way  as  to  appear  to  diverge  from  a  point  on  the  axis  behind  the 
mirror,  which  is  the  principal  focus  of  the  convex  mirror. 

The  distance  from  the  mirror  of  the  point  to  which  parallel 
rays  converge  after  reflection,  or  from  which  they  seem  to  diverge, 
is  called  the  focal  length  of  the  mirror. 

The  focal  length  of  a  mirror,  whether  convex  or  concave, 
is  equal  to  one-half  the  radius. 

In  this  question  where  the  radius  of  the  concave  mirror  is 
said  to  be  3  feet  or  36  inches,  the  focal  length  would  be  1>2  feet 
or  18  inches. 

The  magnification  is  the  ratio  of  the  distance  of  the  image 
from  the  mirror  to  the  distance  of  the  object  from  the  mirror. 
Now,  then,  in  order  that  the  image  may  be  magnified  three  times 
(and  this  magnification  refers  to  linear  dimensions  and  not  to 
area),  its  distance  must  be  three  times  that  of  the  object,  and  in 
this  question  the  focal  distance  of  the  object  and  the  focal 
distance  of  the  image  must  equal  the  focal  length  of  the  mirror, 
which  is  18  inches. 

Let      X  =  distance  of  image 
3  X  =  distance  of  object 

Then4X  =    1 
18 

3    X  =   —  or  — 

72        24 

The  distance  of  the  object  would  be  24  inches  of  the  image 
72  inches. 

And,  inasmuch  as  the  object  is  situated  farther  away  than 
the  focal  distance  of  the  mirror,  the  image  would  be  real. 

A  bright  object  4  inches  high  is  placed  on  the  principal  axis 
of  a  concave  spherical  mirror,  at  a  distance  of  15  inches  from  the 


Theoretic  Optics  91 

mirror;  what  is  the  position  and  size  of  the  image,  the  focal  length 
of  the  mirror  being  6  inches? 

The  first  thing  is  to  determine  the  position  of  the  image, 
as  follows:  119         1 

"6    ~  15   "  90  "  10 

The  image  is  located  at  10  inches. 

Now,  then,  the  distance  of  the  object  is  to  the  size  of  the 
object  as  the  distance  of  the  image  is  to  its  size. 

The  first  three  factors  being  known,  the  fourth  is  determined 
by  the  following  proportion: 

15  :4  :  :  10  :  X 
V     -    ^    X    IQ    _    40    _ 

The  size  of  the  image  is  2  2/3  inches. 


What  is  the  size  and  position  of  the  image  of  an  object  1  inch 
high  placed  respectively  at  distances  of  6  inches,  9  inches,  1  foot, 
and  18  inches  from  a  concave  mirror  9  inches  in  radius? 

If  the  radius  of  the  mirror  is  9  inches,  its  principal  focal 
distance  is  4^  inches. 

If  the  object  is  at  6  inches,  the  image  will  be  at 

J— r  —   —    =  T^  or  18  inches 
4>^         6         18 

Then,  as  the  distance  of  the  image  (18  inches)  is  three  times 
the  distance  of  the  object  (6  inches),  the  size  of  the  image  will  be 
three  times  the  size  of  the  object  or  3  inches. 

If  the  object  is  at  9  inches, 

J L  =  L 

4K       9   ~   9 

the  image  will  be  at  9  inches. 

And  in  this  case,  as  the  distance  of  the  image  is  the  same  as 
the  distance  of  the  object,  the  size  of  the  image  will  be  the 
same  as  the  size  of  the  object,  viz.,  1  inch. 

If  the  object  is  at  12  inches, 

J. }_  ^    \^ 

4^        12        71 

the  image  will  be  at  7  1/5  inches. 


92  State  Board  Examinations 

The  size  of  the  image  is  found  by  the  following  proportion: 

12  :  1  ::  7  1/5  :  X 
^  ^    1    X    7i        3 


12  5 


The  size  of  image  is  3/5  of  an  inch. 
If  the  object  is  at  18  inches, 


J L  =  J.  =   i 

4W        18   ~  18  ~    6 


the  image  will  be  at  6  inches. 

And  as  the  distance  of  the  image  (6  inches)  is  one-third  the 
distance  of  the  object  (18  inches),  the  size  of  the  image  will  be 
one-third  the  size  of  the  object,  or  one-third  of  an  inch. 


What  is  the  difference  between  conjugate  foci  that  are  inter- 
changeable and  those  that  are  not?    Give  examples  of  each. 

Conjugate  foci  are  two  points  so  related  to  each  other  that 
when  the  object  is  at  the  one,  the  image  is  at  the  other. 

If  F  be  the  principal  focal  distance  of  a  mirror,  fi  the  distance 
of  the  object  and  it  the  distance  of  the  image,  then 


1 

F 

1 

°^   F 

1                   1 

fl                  fi 

This  is  an  important  formula  in  optics;  and  fi  and  fo  are 
conjugate  to  each  other  and  are  interchangeable.  If  any  two  are 
known,  the  third  can  always  be  found. 

Suppose  the  focal  length  of  the  mirror  be  8  inches,  and  the 
object  be  placed  at  a  distance  of  40  inches,  then  1/8  would 
represent  the  reflecting  power  of  the  mirror,  and  1/40  the  power 
which  brings  parallel  rays  to  a  focus  at  a  distance  of  40  inches. 
Then 

L  _  1  =  i       J_ 

8         40        40  °*'   10 

And  U  would  be  10  inches  from  the  mirror. 

Therefore,  40  inches  and  10  inches  are  the  distances  of  the 
conjugate  foci  of  this  8-inch  concave  mirror.  If  the  object  be 
placed  at  40  inches,  the  image  will  be  formed  at  10  inches,  and 


Theoretic  Optics  93 

if  the  object  be  placed  at  10  inches,  the  image  will  be  formed 
at  40  inches. 

In  the  above  case  where  the  conjugate  foci  are  interchange- 
able, the  object  is  placed  at  a  greater  distance  than  the  focal 
length  of  the  mirror;  but  if  the  object  be  placed  closer  than  the 
focal  distance  of  the  mirror,  the  conjugate  focus  is  a  negative 
quantity. 

For  instance,  if  we  take  this  same  8-inch  mirror  and  place 
the  object  5  inches  in  front  of  it,  then  we  have 

8  5    ~  40  °''         13 

That  is  the  image  (if  one  could  be  formed)  would  be  13 
inches  behind  the  mirror. 

We  can  prove  this  by  the  formula  - 

i  +  1   =1 
fi         fi  F 

Substituting  figures 

5    ^  V         U   )  8 

Here  —  13  inches  (but  not  13  inches)  is  conjugate  to  5 
inches  with  respect  to  an  8-inch  concave  mirror,  and  5  inches  is 
conjugate  to  —   13  inches,  but  not  to  13  inches. 


What  are  the  laws  of  conjugate  foci  as  they  pertain  to  refracting 

systems? 

1.  In  order  that  the  object  and  image  may  be  interchange- 
able, the  rays  of  light  must  follow  the  same  path  in  both  direc- 
tions. 

2.  If  the  object  is  moved  to  the  right,  the  image  moves  to 
the  right  also;  or  in  other  words,  the  two  foci,  representing  the 
object  and  image,  always  move  in  the  same  direction.  (In  the 
case  of  mirrors  where  the  image  is  formed  by  reflection,  the 
two  foci  move  in  opposite  directions.) 

3.  If  the  rays  proceed  from  a  point  farther  away  than  the 
principal  focus  of  the  lens,  they  will  be  converged  and  the  image 
be  formed  at  the  opposite  side  of  the  lens,  and  will  be  real  and 
inverted. 

4.  If  the  rays  proceed  from  a  point  closer  than  the  principal 
focus,  they  will  be    diverged  as  if  proceeding    from  an   object 


94  State  Board  Examinations 

on  the  same  side  of  the  lens,  and  the  image  will  be  virtual  and 
erect. 

When  parallel  rays  enter  a  convex  lens  and  are  converged, 
we  say  infinity  and  the  principal  focus  are  conjugate. 


Does  a  convex  lens  ever  produce  a  virtual  image?  If  so,  under 
what  conditions? 

When  an  object  is  placed  closer  to  a  lens  than  its  principal 
focal  distance,  the  divergence  of  the  rays  is  so  great  that  the  lens 
is  unable  to  overcome  it,  and  the  rays,  after  passing  through  the 
lens,  would  continue  divergently.  There  would  be  no  real  focus, 
but  a  negative  or  virtual  one,  which  could  be  found  by  drawing 
imaginary  lines  from  the  divergent  rays  backward  to  a  point 
on  the  same  side  of  the  lens  from  which  they  appear  to  come. 

For  instance,  if  an  object  was  placed  10  inches  from  a  20- 
inch  lens,  the  rays  would  enter  the  lens  with  a  divergence  of 
1/10,  which  would  be  partly  neutralized  by  1/20,  the  full  powei  of 
the  lens,  and  they  would  continue  with  a  divergence  of  1/20, 
or  as  if  they  came  from  a  point  20  inches  back  of  the  lens.  Under 
such  conditions  a  convex  lens  produces  a  virtual  image. 


What  are  the  laws  of  reflection  of  light?  The  radius  of  a 
concave  mirror  is  6  feet,  and  a  circular  disk  1  inch  in  diameter  is 
placed  on  the  axis  of  the  mirror  at  a  distance  of  2  feet  from  it. 
Determine  the  size  and  position  of  the  image. 

The  laws  of  reflection  are: 

1.  The  angle  of  incidence  and  the  angle  of  reflection  are 
the  same;  that  is,  the  angle  formed  by  the  incident  ray  with  the 
perpendicular  is  equal  to  the  angle  formed  by  the  reflected  ray 
with  the  perpendicular. 

2.  The  incident  and  the  reflected  rays  lie  in  the  same  plane. 
These  laws  are  true  whatever  be  the  form  of  the  surface, 

whether  plane  or  curved.  Spherical  mirrors  may  be  concave  or 
hollow  toward  the  light,  and  convex  or  bulging  toward  the  light. 
In  regard  to  a  concave  mirror,  if  the  object  be  placed  at 
its  principal  focal  distance,  the  rays  are  reflected  as  parallel  and 
hence  no  image  is  formed. 


Theoretic  Optics  95 

When  the  object  is  located  beyond  the  focal  distance  of  the 
mirror,  the  image  is  real;  and  when  object  is  inside  of  the  focal 
distance,  the  image  is  virtual. 

In  order  to  find  the  position  of  the  image,  we  must  make  use 
of  the  formula  for  conjugate  foci.  If  the  radius  of  the  mirror 
is  6  feet,  the  principal  focus  must  be  3  feet,  or  36  inches. 

If  F  is  principal  focus,  fi  is  distance  of  object,  and  ii  is 
distance  of  image,  then 

i   _  i  =   i 

F  fl  f2 


Substituting  figures 


J-  _  J-  =   i 
36        24        72 


or  72  inches,  or  6  feet. 

Inasmuch  as  the  size  of  the  image  must  be  to  the  size  of 
the  object  as  the  distance  of  the  image  is  to  the  distance  of  the 
object,  and  as  the  image  is  at  6  feet  and  the  object  at  2  feet,  or 
three  times  the  distance,  therefore,  the  image  must  be  three 
times  the  size  of  object,  or  3  inches. 


Practical  Optics 

What  is  the  essential  difference  between  crown  glass  and  flint 
glass? 

Crown  glass  contains  lime,  while  flint  glass  contains  lead. 
On  account  of  the  lead,  flint  glass  possesses  greater  refractive  and 
dispersive  powers.  It  is  denser  and  heavier  than  crown  glass, 
but  softer. 

Crown  glass  is  harder  and  hence  does  not  scratch  so  easily, 
but  at  the  same  time  is  more  brittle.  Crown  glass  also  has  the 
advantage  of  lower  dispersion.  The  index  of  refraction  of  crown 
glass  is  1.52  and  of  flint  glass  1.62. 


Which  fuses  at  the  lower  temperature,  croivn  glass  or  flint 
glass? 

Technically  speaking,  this  depends  upon  the  index  of  refrac- 
tion. The  index  of  crown  glass  may  be  raised  as  high  as  the 
lowest  flint,  or  the  index  of  flint  glass  may  be  lowered  to  the 
highest  crown,  when  they  would  fuse  at  the  same  time. 

But  as  used  in  the  fused  bifocals,  the  flint  fuses  very  much 
sooner  than  the  crown;  otherwise  there  could  not  be  such  a  thing 
as  fused  bifocals. 


Mention  the  properties  that  you  consider  most  essential  -in 
glass  to  be  used  for  making  spectacle  lenses. 

Optical  glass  must  be  homogeneous,  that  is,  of  the  same 
density  and  refractive  power  throughout.  It  should  be  perfectly 
transparent  and  free  from  bubbles,  stride  and  color. 

"In  accordance  therewith  we  have  —  1.75  D.  sph.  O  4.75  D. 
cyl.  axis  160°. 

c  +  .75  D.  sph.  C  -  2.50  D.  D.  cyl.  axis  145°. 

97 


98  State  Board  Examinations 

Hcii'  may  it  he  determined  whether  a  lens  is  spheric  or  cylindric? 

Hold  the  lens  at  some  little  distance  from  the  eye  and  look 
through  it  at  a  straight  line  on  a  card,  or  the  edge  of  a  picture 
frame  or  window  sash.  Rotate  the  lens  or  give  it  a  circular 
motion,  and  if  there  appears  any  break  in  the  line  a  cylinder  is 
shown  to  be  present;  the  break  being  caused  by  the  difference  in 
refraction  of  different  parts  of  the  lens.  If  the  lens  is  a  simple 
sphere  no  break  will  be  caused  in  the  line  by  its  rotation,  because 
a  sphere  has  the  same  curvature  in  all  meridians. 

Care  must  be  taken  to  look  through  the  lens  at  its  optical 
center,  otherwise  the  prismatic  effect  of  the  lens  will  be  brought 
into  action,  and  there  will  be  a  break  in  the  line,  but  in  this 
case  the  part  of  the  line  seen  through  the  lens  will  be  parallel 
with  the  line,  whereas  in  the  case  of  a  cylinder  the  line  as  seen 
through  the  lens  will  be  oblique.  This  illustrates  what  is  known 
as  the  "twisting"  action  of  a  cylinder. 


How  can  the  meridian  of  least  refraction  in  a  sphero-cylinderic 
lens  he  located? 

In  other  words,  find  the  location  of  the  axis  of  the  cylinder. 
Look  through  the  center  of  the  lens  at  a  straight  line  or  edge, 
rotate  the  lens  and  note  the  position  in  which  the  line  is  con- 
tinuous, above,  below,  and  through  the  lens.  Make  an  ink  mark 
on  the  lens  at  this  position,  and  then  place  on  a  protractor  scale 
and  read  off  the  number  of  degrees. 

This  indicates  the  location  of  one  of  the  principal  meridians, 
but  it  may  be  that  of  least  or  of  greatest  refraction,  which  are 
always  at  right  angles  to  each  other.  The  amount  of  motion 
in  these  two  meridians  will  show  at  once  to  the  experienced  eye 
which  one  is  of  least  refraction;  or  if  there  is  any  doubt  about 
it,  each  meridian  may  be  neutralized  in  turn  by  a  spherical  lens. 


Express  in  diopters  the  power  of  a  lens  whose  principal  focal 
distance  is  150  millimeters. 

6.66  D. 


Practical  Optics 

Name  the  various  parts  of  a  spectacle  frame. 
Bridge,  eye  wires,  end  pieces,  screws  and  temples. 


99 


Has  a  lenticular  lens  any  advantage  other  than  lightness? 

We  do  not  know  of  any  other  advantage  except  lightness  and 
better  appearance  as  in  the  doing  away  with  the  thick  edges  of 
strong  concave  lenses.  On  the  other  hand,  there  may  be  some 
disadvantage  from  the  restricted  field. 


What  is  meant  by  a  5°  prism? 

This  means  a  prism  with  a  refracting  angle  of  5°. 


Fig.  18 

What  is  meant  by  the  term  ''base  curve''  as  applied  to  toric 
lenses? 

The  base  curve  is  the  curve  of  least  strength  on  the  toric 
surface;  the  three  most  commonly  used  are  3  D.,  6  D.  and  9  D., 
of  which  6  D.  is  the  one  usually  met  with.    These  are  convex  in 


100  State  Board  Examinations 

most  cases,  although  it  is  sometimes  desirable  to  grind  a  concave 
base  curve. 


How  would  you  determine  the  optical  center  of  a  lens?     The  axis 
of  a  cylinder? 

By  looking  through  a  lens  at  a  straight  line  and  moving  the 
lens  until  the  line  is  continuous  above,  through  and  below  the 
lens.  At  every  other  portion  of  the  lens,  except  the  optical  center, 
the  line  will  appear  broken. 

By  looking  through  a  cylindrical  lens  at  the  same  straight 
line  and  rotating  the  lens.  The  portion  of  the  line  seen  through 
the  lens  will  be  "twisted"  or  broken  by  this  rotation.  Find  the 
portion  of  the  lens  where  there  is  no  break;  this  will  be  one 
principal  meridian,  while  the  one  at  right  angles  will  be  the  other. 
One  of  these  will  be  the  axis  which  can  be  determined  by  motion 
or  by  neutralization,  the  axis  being  plane  and  having  no  power. 


What  is  the  focal  length  of  the  following  lenses  placed  in 
apposition:  +  4  sph.,  +  3  sph.  O  —  -  cyl.  X  75,  +  3.50  sph. 
C  +  i  cyl.  X75,  -  2  sph..  -  4.50  sph.,  -  1  cyl.  X  165? 


+  4.      sph. 

-  2.  cyl 

.  axis    75° 

+  3. 

+  1.     " 

"       75° 

+  3.50     " 

-  1.     " 

"     165° 

-  2. 

-  1.  S. 

-  4.50    " 

+  4.  sph. 

-  1.     " 

+  3.  sph. 

Transpose  the  following: 

To  -h  on  —  equivalent:  +  1.75  sph.  O.  +  2.25  cyl.  X  85 

To  -\-  on  -j-  equivalent:  +  3.50  sph.  3   —1.25  cyl.  X  145 

To  sphero-cyl.form:    +  .75  cyl.  X  90  C   -  2.50  cyl.  X  180 

+  4.  D.  sph.  C  -  2.25  D.  cyl.  axis  175° 
+  2.25  D.  sph.  C  +  1.25  D.  cyl.  axis  55° 
+     .75  D.  sph.  C  -  3.25  D.  cyl.  axis  180° 


Practical  Optics  101 

What  is  the  prismatic  poiver  of  a  5  D.  lens  decentered  3  mm.? 

1   D.  lens  decentered   10  mm.  affords   1°  prismatic  power, 
therefore  5  D.  decentered  3  mm.  develops  \}4°  prismatic  power. 


Give  the  dioptric  value  of  each  surface  of  a  wafer  of  a  cement 
bifocal,  the  distance  correction  being  —  3  sph.  O  -\-  1-50  cyl.  X  90, 
the  addition  being  +  2.50  D. 

+  3  D.  and  -  .50  D. 


In  what  way  does  chromatic  aberration  differ  from  spherical 
aberration? 

Chromatic  aberration  depends  upon  the  varying  degrees 
of  refrangibility  of  the  different  colors  of  which  white  light  is 
composed,  the  violet  coming  to  a  sooner  and  the  red  to  a  later 
focus. 

Spherical  aberration  depends  upon  the  difference  in  refractive 
power  of  the  several  parts  of  a  lens,  the  rays  passing  through 
the  periphery  coming  to  a  sooner  focus  than  those  passing  nearer 
the  center. 


A  plus  lens  has  a  focus  of  30  cm.;  the  index  of  refraction  of 
the  glass  used  is  1.60;  one  surface  is  convex  and  one  a  radius  of 
12  cm.;  what  is  the  nature  and  power  of  the  other  surface? 

If  the  radius  of  curvature  is  12  cm.  and  the  index  of  refrac- 
tion 1.60,  the  focal  length  of  such  a  lens,  if  plano-convex,  is 
20  cm.,  which  makes  the  value  of  the  curvature  of  this  surface 
5  D. 

But  the  lens  itself  having  a  focus  of  30  cm.  has  only  a  value 
of  3.2>?>  D.,  therefore  the  other  surface  of  the  lens  must  be  concave 
1.67  D. 


What  is  the  principal  focus  of  a  lens? 

The  place  or  distance  from  lens  where  parallel  rays  are  made 
to  meet  after  passing  through  such  lens. 


1 02  State  Board  Examinations 

II mv  much  must  a  4  dioptric  lens  be  decentered  so  that  the 
prismatic  action  ivill  be  1%  prism  diopters?  Figure  out  the  same 
by  means  of  a  formida. 

AID.  lens  decentered  10  mm.  develops  1°  prismatic  power; 
a  4  D.  lens  decentered  the  same  distance  shows  4°  of  prismatic 
value.  If  4°  prism  is  developed  by  10  mm.  decentration,  then  the 
desired  1%°  prism  will  be  obtained  by  A^t  of  10;  or  it  may  be 
stated  as  follows:   as  4°  is  to  10  mm.  so  is  \}i°  to  the  answer. 

In  both  cases  the  result  is  3.12  mm. 


With  a  compound  lens,  a  plus  2  sphere  on  a  plus  3  cylinder, 
form  an  image  of  a  distant  arc  light.  As  the  card  is  moved  back  and 
forth  describe  the  appearance  of  the  image  and  the  distance  at  which 
the  most  pronounced  effects  are  reached. 

This  compound  lens  would  show  +  2  D.  power  in  one 
meridian  and  +  5  D.  power  in  the  other;  the  latter  possessing 
the  sharper  curve  would  bring  the  rays  to  a  focus  at  8  inches, 
and  the  former  at  20  inches. 

The  bundle  of  rays  on  account  of  being  more  strongly  re- 
fracted by  one  meridian  would  assume  the  shape  of  an  oval, 
the  long  diameter  being  at  right  angles  to  the  stronger  curve, 
until  finally  they  unite  in  a  focal  line  at  8  inches.  Beyond  this 
point  there  is  a  place  where  the  rays  assume  the  form  of  a  circle, 
and  they  become  oval  in  the  same  direction  as  the  sharper  curve 
and  form  a  focal  line  at  20  inches. 


What  is  the  dioptric  power  of  a  plano-convex  lens,  the  radius 
of  curvature  being  25  cm.  and  the  refractive  index  1.50? 

To  find  the  focal  length  of  a  convex  lens  the  rule  is  to  divide 

the  radius  of  curvature  by  twice  the  index  of  refraction  less  one. 

Rad.  or  curv. 


(2  index  —  1) 
or  substituting  the  figures 


=  focal  length. 


25  cm.  25        ^_ 

=  -;-  =  25  cm. 


2  (1.50  -  1)         1 

Inasmuch  as  a  plano-convex  lens  is  mentioned  and  as  the 
focal  length  of  such  a  lens  is  equal  to  twice  the  length  of  the 


Practical  Optics  103 

radius,  we  multiply  the  above  result  by  two,  which  gives  50  cm. 
as  the  focal  length.  And  as  the  question  asks  for  dioptric  power, 
we  obtain  this  by  dividing  50  cm.  into  1  meter  or  100  cm.,  the 
result  being  2  D.,  which  is  the  answer  asked  for. 


What  is  the  focal  length  of  a  7  D.  lens? 

In  order  to  find  the  answer  to  this  question  in  inches  the 
usual  way  is  to  divide  7  into  40,  on  the  basis  that  40  inches 
equal  one  meter,  but  as  the  exact  figures  are  39.37  inches  to  the 
meter,  in  order  to  be  accurate  we  should  use  these  figures  as 
follows : 

7)39.37 

5.62  inches, 
which  is  the  answer. 

In  order  to  obtain  the  result  in  the  metric  system  we  divide 
7  into  100  cm.,  as  follows: 

7)100 


14.28  cm. 
as  the  answer. 


Which  point  of  the  lens  surface  should  he  determined  before 
cutting  and  mounting  the  lens?  How  is  this  point  to  be  located  and 
what  is  it  called? 

This  has  reference  to  the  optical  center  of  the  lens,  and  is 
located  by  looking  through  the  lens  at  a  straight  line  and  moving 
lens  until  the  line  as  seen  through  and  beyond  the  lens  is  con- 
tinuous and  unbroken.  This  is  done  for  both  vertical  and 
horizontal  meridians,  and  the  point  of  intersection  is  the  optical 
center  and  is  the  point  where  light  passes  through  without 
refraction  at  either  surface. 

It  can  also  be  located  by  looking  through  the  lens  at  the 
vertical  and  horizontal  edges  of  a  card  and  moving  lens  until 
these  edges  are  continuous  through  and  beyond  the  lens,  and 
then  the  corner  of  the  card  will  indicate  the  optical  center. 


104  State  Board  Examinations 

Iratispose  the  following  into  various  possible  forms,  and  state 

which  yon  prefer,  giving  reasons  for  the  preference: 

+  4.00  sph.  +  1.25  cyl.  axis  130° 

+  3.25  sph.  -  1.75  cyl.  axis  110° 

—  2.5-  sph.  +  3.25  cyl.  axis    70° 

T\\e  first  may  be  transposed  into  anothei  sphero-cylinder: 
+  5.25  D.  sph.  C   -  1.25  D.  cyl.  axis  40° 
or  into  a  cross-cylinder: 

+  4  D.  cyl.  axis  40°  C   +  5.25  D.  cyl.  axis  130° 
Some  persons  would  prefer  the  original  formula,  because  it 
is  least  expensive;  while  others  would  give  preference   to   the 
second  formula,  because  of  its  periscopic  shape. 

The  second  may  be  transposed  into  another  sphero-cylinder: 
+  1.50  D.  sph.  C  +  1.75  D.  cyl.  axis  20° 
or  into  a  cross-cylinder: 

+  1.50  D.  cyl.  axis  110°  C  +  3.25  D.  cyl.  axis  20° 
In  this  case  the  original  formula  affords  a  periscopic  shape, 
but  the  second  sphero-cylinder  is  least  expensive. 

The  third  may  be  transposed  into  another  sphero-cylinder: 
+  .75  D.  sph.  C  -  3.25  D.  cyl.  axis  160° 
or  into  a  cross-cylinder: 

+  .75  D.  cyl.  axis  70°  C   -  2.50  D.  cyl.  axis  160° 
In  this  case  both  of  the  sphero-cylinders  are  periscopic,  but 
the  second  one  might  be  preferred  as  being  somewhat  lighter. 


Why  is  it  that  when  an  object  is  viewed  through  a  minus  lens 
and  the  lens  is  moved  up  and  down,  the  object  appears  to  move  in 
the  same  direction? 

At  every  part  of  a  lens,  except  exactly  at  its  optical  center, 
there  is  both  refractive  and  prismatic  power,  the  latter  of  which 
causes  displacement  of  objects  when  viewed  through  the  different 
portions  of  the  lens.  The  displacement  of  an  object  is  always 
in  the  direction  of  the  apex  of  the  prism  and  in  a  concave  lens 
the  apex  is  at  the  center;  hence,  when  the  center  of  the  lens  is 
moved  up,  an  object  viewed  tl^^ough  it  moves  up  also;  when 
moved  down,  object  moves  down.  Therefore,  with  a  concave 
lens  the  movement  is  always  in  the  same  direction  as  the  lens. 


Practical  Optics  105 

Describe  a  toric  lens. 

A  toric  lens  is  one  in  which  one  of  the  surfaces  is  toroid. 
A  toroid  surface  is  one  that  shows  two  curvatures  like  the  bowl 
of  a  spoon,  the  greater  curvature  being  at  right  angles  to  the 
lesser.  This  affords  the  effect  of  a  sphero-cylinder  all  on  one 
surface.     The  other  surface  is  ground  in  a  deep  meniscus  form. 


What  is  a  meniscus  lens? 

Meniscus  comes  from  a  Greek  word,  meaning  crescent,  and  is 
applied  to  lenses  that  are  ground  concave  on  one  surface  and 
convex  on  the  other. 

Name  several  styles  of  bifocals,  with  a  brief  description  of 
the  same. 

Cemented,  bisight.  Kryptok  and  Ultex. 

In  the  cemented  form  the  distance  lens  is  of  full  size,  and 
the  addition  necessary  for  reading  is  made  by  means  of  a  thin 
wafer  or  segment,  which  is  cemented  on  by  means  of  Canada 
balsam  to  the  lower  portion  of  the  large  lens. 

In  the  bisight  and  Ultex  forms  the  necessary  curves  for 
distance  and  reading  are  ground  on  a  single  piece  of  glass. 

In  the  Kryptok  form  the  large  lens  is  made  of  crown  glass 
and  the  small  lens  of  fhnt.  and  the  two  fused  on  account  of  the 
difTerence  in  their  refracti\e  indices;  it  is  a  matter  of  calculation 
to  obtain  the  desired  reading  power. 


Name  the  parts  of  an  eyeglass. 
Spring,  guards,  studs  and  straps. 


What  is  the  dioptric  power  of  a  lens  that  focuses  parallel  rays 
of  light  at  10  cm.? 


10  D. 


How  can  you  ascertain  if  a  lens  has  been  properly  centered? 
By  looking  through  the  lens  at  a  straight  line  or  a  cross  on 


106 


State  Board  Examinations 


a  lar^e  card  within  a  few  feet,  or  hanging  on  the  wall  across  the 
room.  With  a  convex  lens,  if  weak,  these  lines  may  be  placed  at 
almost  any  distance,  but  if  the  convex  lens  is  strong  the  distance 
must  be  correspondingly  shortened.  Another  point  of  importance 
is  that  the  lens  must  not  be  held  too  close  to  the  eye  of  the 
observer — not  closer  than  ten  inches,  and  better  if  at  arm's 
length. 

The  position  of  the  lens  is  then  shifted  and  moved  to  that 
place  where  the  lines  are  continuous  vertically  and  horizontally 
through  and  beyond  the  lens;  in  other  words,  where  there  is  no 
break  in  the  lines.  If  the  point  of  crossing  of  the  lines  agrees 
with  the  mechanical  or  geometrical  center,  the  lens  is  properly 
centered;  otherwise  not.  The  optical  center  is  indicated  by  the 
crossing  of  the  lines,  and  it  can  be  quickly  seen  if  this  is  in  the 
proper  position  or  not. 


If  your  trial  case  contained  only  spherical  lenses,  how  could 
you  determine  the  powers  of  the  component  elements  of  a  given 
sphero-cylindric  lens? 

With  a  sphero-cylindrical  lens  there  is  motion  in  all  directions 
and  I  would  first  notice  if  the  movement  is  with  or  against.  In 
this  way  I  would  determine  if  the  lens  was  convex  or  concave, 
so  as  to  be  able  to  pick  out  a  neutralizing  lens  of  the  opposite 
kind. 


I  D. 


—  2  D. 


+  1  D. 


-I-  2  D. 


Neutralizing  Lenses 


Fig.  19 


Power  of  Lens 


There  is  one  meridian  in  which  motion  is  greatest  and  one 
meridian  in  which  it  is  least,  and  in  order  to  locate  these  two 
meridians  I  would  look  through  the  lens  at  a  line  or  a  straight 
edge  and  rotate  it.     There  are  two  positions,  and   two  only. 


Practical  Optics  107 

where  the  edge  is  unbroken,  and  these  indicate  the  location  of 
the  meridians  of  least  and  greatest  curvature. 

I  would  then  find  a  lens  that  would  destroy  the  motion  in 
the  meridian  of  least  curvature  and  another  lens  to  neutralize 
the  meridian  of  greatest  motion.  The  weaker  lens  would  be  the 
sphere,  and  the  difference  between  the  two  the  cylinder  with  its 
axis  in  the  direction  of  the  weakest  meridian. 

Suppose  the  two  principal  meridians  were  vertical  and  hori- 
zontal and  a  —  1  D.  neutralized  the  former  and  a  —  2  D.  the 
latter. 

Then  the  value  of  the  lens  we  were  neutralizing  would  be 
+  1  D.  sph.  C   +  1  D.  cyl.  axis  90° 

What  is  the  characteristic  difference  between  a  plane  cylindric 
lens  and  a  sphero-cylindric  lens? 

In  the  former  one  surface  is  piano  and  the  other  ground 
cylindrical.  In  the  latter  both  surfaces  are  curved,  one  being 
ground  on  a  spherical-shaped  tool  and  the  other  on  a  cylinder- 
shaped  instrument. 

In  the  sphero-cylinder  all  meridians  have  power  varying  in 
degree;  in  the  piano-cylinder  there  is  one  meridian  without  power 
— that  is,  in  the  direction  of  its  axis. 


How  are  lenses  for  optometric  practice  usually  numbered? 

There  are  two  systems  by  which  lenses  are  numbered — the 
older,  or  inch  system,  which  shows  the  focal  distance  of  the  lens, 
and  the  newer  and  better  system,  the  dioptric  or  metric,- which 
expresses  the  refractive  power  of  the  lens. 

Explain  the  dioptric  system  of  numbering  and  measuring 
lenses. 

The  standard  of  measurement,  or  the  unit  of  the  dioptric 
system,  is  a  lens  of  1  D.,  which  has  a  focal  distance  of  one  meter. 
This  lens  is  comparatively  weak  and  the  stronger  lenses  in  com- 
mon use  are  multiples  of  this  unit.  Weaker  lenses  than  the  unit 
are  expressed  in  decimal  fraction,  one-quarter,  one-half  and 
three-quarters  of  a  diopter  being  written  .25  D.,  .50  D.,  and 
.75  D. 


108  State  Board  Examinations 

The  power  of  any  lens  expressed  in  diopters  is  the  reciprocal 
of  its  principal  focus  expressed  in  meters;  as,  for  instance,  a  2  D. 
lens  has  a  focal  distance  of  half  a  meter,  a  lens  of  4  D.  of  one- 
quarter  meter. 

The  two  chief  objects  urged  against  the  inch  system — the 
difificulty  of  combining  vulgar  fractions  and  the  irregular  intervals 
between  the  lenses — are  entirely  removed  in  the  dioptric  system, 
where  the  decimal  fractions  can  be  as  easily  added  and  sub- 
tracted as  whole  numbers  and  where  there  is  a  regular  graduation 
of  increase  of  .25  D.  

What  prismatic  power  would  be  produced  by  decentering  a 
4  D.  spherical  lens  5  mm.? 

The  rule  of  decentration  is  as  follows :  For  every  decentration 
of  10  mm.  there  will  be  as  many  degrees  of  prismatic  power  as 
there  are  diopters  of  refractive  power. 

Therefore,  a  4  D.  lens  decentered  10  mm.  would  develop  a 
prismatic  value  of  4°;  but  as  the  question  names  a  decentration 
of  5  mm.  the  prismatic  power  would  be  one-half  of  the  amount 
named,  or  2°.  

Name,  with  respect  to  their  curvatures,  the  different  kinds  of 
lens  surfaces  used  in  optometric  practice. 

The  surfaces  may  be  enumerated  as  convex,  concave, 
spherical,  cylindrical  and  toric. 

Prisms  are  sometimes  used  in  optometric  practice,  but  the 
surfaces  of  prisms  (if  uncombined  with  other  lenses)  are  plane, 
not  curved.  

How  is  it  possible  to  tell  the  principal  focus  of  a  concave  lens 
without  the  use  of  neutralizing  or  other  lenses,  and  without  the  use 
of  a  lens  measure? 

The  lens  is  to  be  held  in  such  a  position  in  front  of  a  screen 
that  the  rays  from  a  distant  source  of  light  as,  for  instance,  the 
sun,  will  pass  through  it  and  fall  upon  the  screen.  A  central 
dark  spot  will  be  seen  upon  the  screen  with  an  area  of  brightness 
surrounding  it. 

The  lens  is  then  moved  to  and  from  the  screen  until  a  point 
is  found  where  the  area  of  brightness  is  twice  the  diameter  of 


Practical  Optics  109 

the  concave  lens,  and  then  measure  the  distance  of  the  lens  from 
the  screen,  which  will  be  the  principal  focal  distance  of  the  lens. 


How  would  you  he  able  to  tell  whether  a  prescription  for  a 
prism  has  been  filled  with  the  amount  of  prism  ordered;  no  more, 
no  less? 

In  the  first  place,  we  could  tell  by  neutralizing  the  prism 
with  one  from  the  trial  case,  placing  base  over  apex.  For  in- 
stance, if  we  found  that  the  line  was  broken  and  that  the  part 
seen  through  the  lens  was  deflected  to  right,  we  would  know  a 
prism  was  present  and  that  its  base  was  to  the  left.  We  take  a 
prism  from  the  test  case,  placing  it  base  to  the  right  and  changing 
the  prism  until  we  found  one  that  restored  the  break  in  the 
line  and  made  it  continuous,  above,  below^  and  through  the  lens. 

Or  we  can  make  use  of  our  knowledge  of  the  fact  that  rays 
are  deflected  in  the  proportion  of  1  cm.  for  each  meter  of  distance. 
For  this  purpose  we  have  a  card  showing  a  series  of  parallel  lines 
which  are  numbered  and  separated  by  an  interval  of  1  cm. 

Then  we  hold  the  prismatic  lens  over  these  lines  and  note 
the  arnount  of  displacement  and  this  will  show  the  strength  of 
the  prism. 

Suppose  we  have  a  series  of  vertical  lines  numbered  from 
left  to  right,  9,  8,  7,  6,  5,  4,  3,  2,  1,  0.  and  equidistant  from  each 
other.  The  end  or  O  line  on  the  right  is  made  longer  than  the 
others  and  at  its  foot  is  placed  an  X.  The  prismatic  lens  is  held 
with  its  base  to  the  right,  and  the  X  on  the  O  line  is  viewed 
through  it,  when  it  will  be  seen  that  the  X  has  been  displaced 
to  the  left  and  coincides  with  the  line  marked  3,  which  represents 
the  strength  of  the  prism. 

If  the  prism  is  held  at  a  distance  of  1  meter  the  lines  should 
be  1  cm.  apart;  if  a  distance  of  half  a  meter,  then  ^  of  a  cm. 
apart,  and  this  ratio  must  be  always  maintained  or  the  accuracy 
of  the  measurement  is  destroyed. 


Transpose  the  following  toric  lens:    Minus  surface  5  D.,  plus 
surface  6  and  +  7 .50. 

+  1  D.  sph.  C   +1.50  D.  cyl. 


110  Slate  Board  Examinations 

A  lens  measure  made  to  measure  lenses  made  of  glass  with  a 
refractive  index  of  1.52  shows  one  side  of  a  lens  to  be  —  1.25  and 
the  other  to  be  +  2.75,  but  the  glass  of  ivhich  this  particular  lens 
is  made  has  an  index  of  refraction  of  1.62;  what  will  be  the  radius 
of  curvature  of  a  plano-convex  lens,  with  an  index  of  refraction  of 
1.52,  which  will  have  the  same  effect  on  light  as  the  first-mentioned 
lens? 

The  lens  measure  shows  this  lens  to  be  a  periscopic  convex 
lens  of  1.50  D.  when  used  on  glass  with  an  index  of  refraction  of 
1.62,  but  as  this  lens  measure  was  made  to  measure  glass  with  a 
refractive  index  of  1.52,  there  would  be  a  corresponding  in- 
crease in  the  refractive  power  of  the  lens,  as  shown  by  the  follow- 
ing proportion: 

.52  :  .62  ::  1.50  :X 
in  which  case  X   =    1.78  D.,  which  represents  the  real  value  of 
the  lens. 

Now,  then,  the  question  to  be  solved  is,  what  is  the  radius 
of  curvature  of  a  lens  of  this  power  with  an  index  of  refraction 
of  1.52?  In  order  to  obtain  this  we  multiply  focal  distance  by  the 
index  of  refraction,  less  unity.  The  focal  distance  of  a  +  1-78  D. 
lens  is  approximately  22  inches.  The  problem  is  22  x  .52  =  11.44 
inches,  which  is  the  radius  of  curvature  of  the  lens. 


How  is  it  possible  to  measure  approximately  the  strength  of  a 
biconcave  lens  without  either  neutralizing  lenses  or  a  lens  measure? 

By  using  the  surfaces  of  the  lens  as  concave  mirrors  and 
then  make  calculations  on  the  principle  that  the  focal  length  of  a 
concave  mirror  is  equal  approximately  to  one-half  the  radius  of 
curvature. 

For  instance,  if  each  surface  of  the  lens  focuses  light  by 
reflection  at  a  distance  of  two  inches,  then  the  radius  of  curva- 
ture of  each  surface  would  be  4  inches,  equivalent  to  a  10  D.  value. 

If  the  index  of  refraction  of  the  glass  is  1.50  then  the  problem 
is: 

(-  1.50  -  1)    (-  10  D.  +  -  10  D.) 
or  .50  X  -  20  D.  =  10  D. 

which  would  be  the  approximate  measure  of  strength  of  such 
biconcave  lens. 


Practical  Optics  111 

In  looking  through  a  lens  at  a  small  distant  object,  and  moving 
the  lens  from  side  to  side,  the  distant  object  seems  to  have  movement; 
what  is  the  reason  for  this? 

At  the  optical  center  of  a  lens  the  two  surfaces  are  parallel 
for  a  very  minute  point,  and  as  a  result  the  axial  ray  passes 
unrefracted.  As  the  optical  center  is  departed  from  the  surfaces 
show  a  curve  which  results  in  the  development  of  refractive  and 
prismatic  power,  increasingly  so  from  center  to  periphery. 

As  the  lens  is  moved  from  side  to  side  before  an  eye  which 
is  fixed  on  some  distant  object,  the  visual  line  passes  through 
different  parts  of  the  lens,  each  in  succession  showing  prismatic 
power  in  the  same  direction.  Now  the  effect  of  a  prism  is  to 
cause  displacement  of  an  object  looked  at,  and  it  is  impossible 
to  view  an  object  through  a  prism  without  such  displacement 
becoming  noticeable. 

The  displacement  is  always  in  the  direction  of  the  apex 
of  the  prism  and  hence  in  a  convex  lens,  where  the  apex  is  at  the 
periphery,  the  motion  is  opposite ;  while  with  a  concave  lens,  where 
the  apex  is  at  the  center,  the  motion  is  with. 


Under  what  circumstances  will  two  strong  lenses,  one  minus 
and  the  other  plus,  each  of  the  same  curvatures,  neutralize  each  other? 

With  strong  lenses  it  is  almost  impossible  to  get  perfect 
neutralization,  but  the  thinner  the  lenses  the  more  we  can 
approximate  neutralization.  Also  if  the  lenses  to  be  neutralized 
are  piano-spheres,  so  that  the  two  plane  surfaces  can  be  placed 
in  apposition.  There  is  difficulty  in  finding  neutralization  all 
over  the  lens,  especially  in  the  peripheral  portions,  on  account  of 
spherical  aberration.  But  as  the  center  of  the  lens  is  the  portion 
patient  looks  through,  this  is  the  part  of  the  lens  to  which  most 
attention  is  given  in  neutralizing. 


Explain  the  effect  of  spherical  and  chromatic  aberration  in 
lenses  for  spectacles  and  eyeglasses. 

In  the  weaker  numbers  of  glasses  that  are  used  for  spectacles, 
aberration  is  so  slight  that  it  can  practically  be  ignored.  In  the 
stronger  numbers  used  in  telescopes  and  microscopes,  aberration 
must  be  and  is  corrected. 


112  State  Board  Examinations 

The  effect  of  spherical  aberration  is  to  cause  the  wandering 
of  rays  from  a  single  focus  and  thus  make  it  more  or  less  diffuse, 
while  the  effect  of  chromatic  aberration  is  to  cause  an  unequal 
refraction  of  colors  and  thus  give  the  focus  a  fringe  of  rainbow 
colors. 


Name  some  important  points  in  a  spectacle  lens. 

It  should  be  perfectly  clear  and  transparent,  absolutely 
without  specks,  flaws  or  bubbles,  and  surfaces  well  polished. 
It  should  be  of  the  proper  size  to  correspond  to  the  pupillary 
distance,  correctly  centered  to  meet  the  visual  axes  and  light  in 
weight. 


/;/  how  many  different  ivays  can  a  sphero-cylinder  he  made  up? 

There  are  always  two  ways  in  which  a  sphero-cylinder  can 
be  made  up,  one  in  which  the  cylinder  is  convex  and  the  other 
in  which  it  is  concave,  the  axis  of  cylinder  in  the  two  ways  being 
at  right  angles  to  each  other.  The  prescription  can  also  be  made 
up  in  the  form  of  a  toric  to  give  the  same  effect:  although  then 
it  is  not,  strictly  speaking,  a  sphero-cylinder. 


Why  is  the  image  of  a  point  formed  by  a  cylinder  a  line  and 
not  a  point? 

The  bundle  of  rays  as  they  strike  the  lens  may  be  represented 
by  a  circle.  If  the  lens  be  a  sphere  with  equal  powder  in  all  me- 
ridians, the  circle  will  be  focused  to  a  point. 

If  the  lens  be  a  cylinder  with  no  power  in  the  meridian  of 
its  axis,  the  light  will  be  subject  to  the  action  of  the  meridian  at 
right  angles,  and  as  the  rays  are  converged  by  this  one  meridian 
only  they  are  brought  to  a  focal  line  in  the  same  meridian  as  the 
axis. 


//  a  compound  lens,  minus  on  minus,  were  placed  before  you 
with  the  axis  of  the  cylinder  set  with  an  inclination  somewhere 
betiveen  90°  and  180°,  state  hoiv  you  ivould  determine  by  simply 
looking  through  the  lens  at  the  crossbars  of  a  window  frame,  that 


Practical  Optics 


113 


the  axis  was  not  between  zero  and  90°.     Illustrate  your  answer  with 
a  diagram. 

If  a  straight  line  be  looked  at  through  a  cylindrical  lens, 
either  simple  or  compound,  the  line  will  appear  straight  in  only 
two  positions  of  the  lens,  the  meridian  of  its  axis  and  the  meridian 
at  right  angles  to  its  axis.  In  all  other  positions  the  line  will  be 
inclined   to  one  side  or  the  other.      Hence,   in   looking  at   the 


Showing  Displacement  of  a  Straight  Line  by  Rotation  of   a  Cylinder 

Fig.  20 

crossbars  of  the  window,  they  would  appear  broken  if  the  axis . 
of  the  cylinder  was  oblique,  whereas  if  the  axis  was  at  90°  or  180° 
the  crossbars  would  be  continuous  beyond  and  through  the  lens. 

Transpose  the  following  into  a  resultant  prism,  and  indicate 
the  angle  of  inclination  of  the  base-apex  line  in  standard  notation 
or  by  diagrams:   R.  E.  2%°  prism  base  in;  1°  prism  base  up. 


114  State  Board  Examinations 

We  make  a  diagram  drawing  straight  lines  proportional  in 
length  to  the  deviating  powers  of  the  prisms,  arranged  according 
to  the  directions  in  which  the  apices  of  the  prisms  point. 

In  this  case  we  ha\'e  a  prism  2%°  base  in,  which  is  repre- 
sented by  a  horizontal  line  2%  cm.  long  as  the  deviating  power 

Fig.  21. 

of  the  prism  towards  the  right.  From  the  base  of  this  prism  we 
draw  a  vertical  line  1  cm.  long  to  represent  the  deviating  power 
of  the  prism  downward.  The  strength  of  the  resultant  prism 
is  2}4°  as  indicated  by  the  length  of  the  dotted  line,  which  is 
2^  cm.,  and  the  inclination  of  its  base-apex  line  can  be  found 
by  comparing  with  a  protractor. 


What  advantage  has  a  periscopic  lens  over  a  double  convex  or 
concave  lens  mounted  in  spectacles? 

The  usual  form  of  periscopic  lens  is  ground  with  what  might 
be  called  a  base  curve  of  1.25  D.  In  periscopic  convex  lenses 
the  concave  curve  is  1.25  D.  In  periscopic  concave  lenses  the 
convex  curve  is  1.25  D. 

The  special  advantages  claimed  for  periscopic  lenses  are  that 
■they  conform  to  the  front  convex  surface  of  the  eye,  allowing 
the  lenses  to  be  brought  closer  to  the  eye  and  still  leave  room 
for  the  play  of  the  lashes,  and  also  to  prevent,  as  far  as  possible, 
the  cylindrical  effect  that  is  developed  w^hen  the  visual  line  passes 
obliquely  through  the  lens. 

But  it  has  long  since  been  recognized  that  the  usual  peri- 
scopic lenses  presented  these  advantages  but  imperfectly,  and 
this  led  to  the  manufacture  of  the  deep  meniscus  or  toric  lenses, 
with  a  concave  curve  of  6  D.  or  more,  w^hich  are  fulfilling  the 
requirements  for  periscopic  lenses  and  are  growing  rapidly  in 
popular  favor,  notwithstanding  their  greater  expense. 


Which  surface  of  a  -\-  3  D.  sph.  Z^    -\-  1  D.  cyl.  should  be 
placed  nearer  the  eye? 


Practical  Optics  115 

The  rule  is  to  place  the  greatest  concave  or  the  least  convex 
surface  next  to  the  eye  and  in  accordance  therewith  the  +  1  D. 
cylindrical  surface  should  face  inwards. 

Perhaps  it  would  be  better  to  transpose  this  lens  into  a  +  4 
D.  sphere  C  —  D.  cyl.  and  place  the  concave  cylindrical  surface 
next  to  the  eye. 

What  is  the  effect  in  strong  plus  lenses  of  having  them  set 
nearer  to  the  eyes  in  the  frames  than  they  were  in  the  test  with  the 
trial  case  lenses? 

A  convex  lens  when  set  closer  to  the  eyes  loses  in  effective 
power.  In  the  ordinary  lenses  the  change  is  scarcely  enough  to 
be  considered,  but  in  strong  lenses  it  might  be  well  to  take  it 
into  account. 


What  difference  should  there  he  in  the  position  of  distance  and 
reading  glasses? 

The  optical  centers  of  reading  glasses  should  be  a  little 
closer  and  a  little  lower  than  for  distance.  The  plane  of  the 
glasses  should  be  vertical  in  distance  glasses,  while  for  reading 
they  should  be  angled  slightly  forward,  so  that  in  each  case  the 
visual  line  may  be  at  right  angles  to  the  plane  of  the  lenses. 


How  is  a  riding  frame  manipulated  if  one  ear  is  higher  than 
the  other? 

The  temple  on  this  side  should  be  bent  upwards  close  to  joint, 
which  will  result  in  lowering  this  lens  and  make  them  both  of 
the  same  height. 

Can  a  prismatic  effect  be  produced  by  glasses  that  are  properly 
centered? 

If  the  glasses  w^ere  properly  centered  for  distance  there 
would  be  some  prismatic  effect  at  the  reading  point;  and  if 
properly  centered  for  reading  there  would  be  some  prismatic 
effect  at  distance.     In  other  words,  there  is  bound  to  be  some 


1  U)  State  Board  Examinations 

prismatic  effect  when  glasses  are  used  at  a  distance  different  from 
that  for  which  thev  are  centered. 


What  measurements  must  be  taken  in  fitting  spectacles  to  face? 

Pupillary  distance,  height  of  bridge,  width  of  base  and 
inclination  of  bridge.  To  these  may  be  added  temple  width 
and  temple  length. 

In  a  case  where  a  strong  concave  lens  is  required  (say  14  D.), 
but  the  nose  is  sensitive  to  the  iceight  of  the  glasses,  what  form  of  lenses 
can  be  supplied  which  will  reduce  the  weight  to  the  minimum? 

Flattened  face  lenses  in  which  the  thick  peripheral  edge  is 
ground  down;  or  lenticular,  in  which  a  small  scale  is  cemented 
on  a  larger  lens. 

A  prescription  reads  +  1.50  for  distance  and  +  4  D.  for 
near.  The  distance  glass  is  supplied  in  the  standard  periscopic 
form.  What  will  be  the  power  of  each  side  of  the  ivafer  as  shown 
by  the  lens  measure  ? 

In  a  periscopic  con\"ex  lens  the  standard  concave  surface  is 
1.25,  on  which  the  wafer  is  cemented.  Hence  its  one  surface 
must  be  +  1.25  to  correspond  to  the  surface  to  which  it  is 
cemented,  and  its  other  surface  +  1.25  to  make  up  the  2.50  D. 
that  is  to  be  added  to  the  distance  glass. 

In  using  a  lens  measure  we  cannot  place  its  points  against 
the  cemented  surface  of  the  wafer,  but  we  can  place  them  against 
the  surface  of  the  distance  lens,  and  we  know  they  must  both 
be  of  same  value  but  of  opposite  curves.  If  the  w^afer  is  large 
enough  we  can  place  the  points  of  the  lens  measure  against  its 
other  surface,  and  thus  we  are  able  to  ascertain  the  curvature 
of  both  surfaces  of  the  wafer 


Given  a  plus  compound,  explain  three  ways  in  which  the  two 
meridians  can  be  located  and  the  poiver  of  the  compound  measured 
or  calculated. 

The  easiest  way  would  be  by  the  lens  measure.  The  most 
accurate  way,  but  involving  a  little  more  trouble,  would  be  by 
neutralization  by  a  similar  minus  compound 

Also  by  looking  through  the  lens  at  a  line  or  a  cross  and 
locating  the  principal  meridians,  and  then  neutralizing  each  in 


Practical  optics  117 

turn  by  a  minus  sphere.     Obtaining  thus   the  power  of  each 
meridian,  transposition  is  made  to  a  sphero-cylinder. 


How  can  a  toric  lens  he  made  and  yet  not  he  periscopic  ? 

Notwithstanding  a  popular  notion  to  that  effect,  a  toric 
lens  does  not  necessarily  mean  a  periscopic  shaped  lens.  The 
word  toric  implies  that  two  curvatures  are  ground  on  one  surface, 
as  instanced  in  the  under  surface  of  the  bowl  of  a  spoon.  The 
other  surface  of  the  lens  may  be  flat  or  convex,  according  to  the 
fancy  of  the  prescriber,  but,  as  a  matter  of  fact,  it  has  been 
found  con\'enient  to  grind  one  surface  deeply  concave,  but  this 
is  not  essential  to  a  toric  lens.  Of  course,  it  is  understood  that 
if  one  surface  is  made  concave  the  convexity  of  the  other  surface 
must  be  correspondingly  increased. 

If  it  was  desired  to  grind  +  1  D.  sph.  O  +  -50  D.  cyl. 
axis  90°  in  a  toric  form  we  could  have  the  toric  surface  +  .50  D. 
in  one  meridian  and  +  1  D.  in  the  other  meridian,  and  the  second 
surface  +  .50  D.  in  all  meridians.  This  would  constitute  a 
toric  lens,  but  it  would  not  be  periscopic. 


What  is  an  achromatic  lens  and  on  what  principle  is  it  made? 

The  dispersive  power  of  lenses  is  not  always  in  proportion 
to  their  refractixe  power.  The  refraction  of  crown  glass  is  in 
relation  to  its  dispersion  as  152  is  to  203,  while  of  flint  glass  the 
ratio  is  162  to  433.  This  shows  the  high  dispersive  power  of 
flint  glass. 

These  facts  are  made  use  of  in  the  manufacture  of  achromatic 
lenses,  which  are  a  combination  of  these  two  different  kinds  of 
glass,  so  proportioned  that  the  dispersion  of  the  convex  lens 
shall  be  neutralized  by  the  concave  lens,  but  not  all  of  its  refrac- 
tive power,  with  the  result  of  making  a  refractive  lens,  robbed  of 
its  dispersi\'e  power,  able  to  make  an  image  without  colored 
edges.  In  such  a  combination  the  convex  lens  is  of  crown  glass 
and  the  conca\'e  lens  of  flint  glass. 


What  is  the  advantage  of  the  meniscus  form  of  lenses? 

With  flat  lenses,  as  the  eyes  turn  up  and  down,  in  and  out, 
the  line  of  vision  passes  obliquely  through  the  lenses,  causing  an 
added  cylindrical  effect.     This  is  to  a  great  extent  obviated  by 


118 


State  Board  Examinations 


the  meniscus-shape  lenses,  whose  concave  surface  corresponds 
to  some  extent  to  the  convex  surface  of  the  eye,  thus  affording 
better  vision  as  the  eyes  turn  in  different  directions.  Also  they 
can  be  brought  closer  to  the  eyes  and  thus  shut  out  many  reflec- 
tions.   

What  is  the  rule  for  the  decentering  of  lenses?  If  a  5  D.  sphere 
is  decentered  3  mm.,  what  will  he  the  prismatic  effect? 

For  every  decentration  of  10  mm.  there  are  as  many  degrees 
of  prismatic  power  as  there  are  diopters  of  refractive  power. 
A  5  D.  lens  decentered  10  mm.  would  show  5  prism  diopters, 
and  decentered  3  mm.  would  be  3/10  of  vS  =  1>2  prism  diopters. 


The  finding  of  a  certain  case  is  0.  U.  +  50  sphere,  combined 
w'ith  -f-  75  D.  cylinder  axis  90°.  These  are  ordered  in  torics  on 
a  -\-  6  base  curve.  What  will  the  leiis  measure  show  on  the  t%vo  stir- 
faces  of  the  lens  when  completed  and  in  the  mountings? 


^5o, 

Curves  in  aphero-cyliuder  Curves  in  Toric  form 

Fig.  22. 


If  +  6  D.  is  to  be  the  base  curve  it  is  the  lowest  curve  on 
the  toric  surface,  which  would  be  the  vertical  meridian,  and 
-f  6.75  in  the  horizontal  meridian.  Then,  in  order  to  afford  the 
desired  power  in  both  meridians,  a  —  5.50  D.  curve  is  ground  on 
the  inner  surface. 


Practical  Optics  119 

The  following  pair  of  lenses  are  ground  on  a  -\-  7 .50  D.  base 
curve: 

(a)  R.  E.,  -  2.25  D.  S.  =  +  3.25  D.  C.  axis  15°; 

(b)  L.E.,  -  1.75  D.  S.  =  +  3.75  D.  C.  axis  145°. 

Give  all  the  curves  of  the  lenses  in  their  principal  meridians, 
indicating  them  on  crosses. 

Write  an  order  for  riding  bow  frames,  giving  all  the  dimensions 
for  a  patient  with  a  narrow  pupillary  distance  and  a  broad  nose. 

Pupillary  distance,  2  3/16  inches;  height  bridge,  1/16 
inch;  inclination  of  bridge,  1/16  inch;  in  width  base  of  bridge, 
13/16;  0  eye. 

If  you  should  order  a  -\-  1  D.  sphere  combined  with  a  —  1.50 
cylinder  axis  90°  in  the  form  of  a  toric  lens,  what  would  you  find 
on  checking  up  the  glasses  with  a  lens  measure? 

Unless  otherwise  ordered,  the  toric  curves  are  usually  on 
the  convex  surface  and  the  base  curve  is  +  6  D. 

On  the  outer  surface  there  would  be  +  6  D.  curve  in  the 
horizontal  meridian  and  +  7.50  D.  curve  in  the  vertical  meridian. 
On  the  inner  surface  there  would  be  —  6.50  D.  in  all  meridians. 


If  you  should  order  a  -\-  1  D.  sphere  combined  with  a  —  1.50 
cylinder  axis  90° ,  the  same  to  be  made  in  the  toric  form  and  on  a 
base  curve  of  —  6  D.,  what  would  you  find  with  the  lens  measure? 

On  the  inner  surface  there  would  be  a  —  6  D.  curve  vertically 
and  a  —  7.50  D.  horizontally.  On  the  outer  surface  there  would 
be  +  7  D.  in  all  meridians. 


How  is  the  optical  center  of  a  lefis  found? 

By  holding  the  lens  some  little  distance  from  the  eye  and 
looking  through  it  at  a  straight  line  and  moving  the  lens  until 
the  line  is  continuous  above,  through  and  below  the  lens.  This 
is  repeated  with  the  lens  turned  quarter  way  around,  and  the 
point  of  intersection  of  the  two  lines  will  indicate  the  location 
of  the  optical  center.    Or  a  cross  may  be  used  and  the  lens  moved 


120  State  Board  Examinations 

until  the  arms  ^lrc  continuous  without  and  within  the  lens,  and 
the  intersection  of  the  arms  of  the  cross  will  indicate  the  optical 
center. 


State  the  powers  as  showji  by  a  lens  measure  in  the  case  of  a 
toric  lens  -\-  8  D.  sph.  O  +  -  O'^-  ^•'^^•^  ^0°,  the  toric  being  made 
with  a  base  curve  of  +  6.     Will  such  a  lens  be  a  meniscus? 

On  the  outer  surface  there  will  be  +  6  D.  power  in  the 
vertical  meridian  and  +  8  D.  power  in  the  horizontal  meridian. 
On  the  inner  surface  there  will  be  a  +  2  D.  power  in  all  meridians. 
This  is  not  a  meniscus  lens. 


What  is  the  advantage  of  the  metric  system  of  7nimbering  lenses? 

It  does  away  with  all  the  disadvantages  of  the  inch  system. 
The  unit  being  comparatively  weak  the  stronger  numbers  are 
multiples  of  the  unit  and  can  be  expressed  in  whole  numbers. 
There  are  no  vulgar  fractions  to  be  added  or  subtracted,  but 
instead  there  are  decimals  w^hich  are  easy  of  manipulation.  The 
interval  between  the  lenses  is  regular,  it  expresses  the  dioptric 
power  of  the  lens  instead  of  its  focal  distance,  and  it  is  a  uniform 
system  all  over  the  world. 


State  the  powers  as  shoivn  by  a  lens  measure  in  the  case  of  a 
toric  lens  -\-  8  D.  sph.  O  +  ^  cyl.  axis  90° ,  the  toric  lens  being  made 
on  a  base  curve  of  —  6  D.     Will  such  a  lens  be  a  meniscus? 

On  the  inner  or  toric  surface  —  6  D.  power  in  horizontal 
meridian  and  —  8  D.  power  in  vertical  meridian. 

On  the  outer  surface  +  16  D.  pow'er  in  all  meridians. 
This  lens  will  be  a  meniscus. 


How  many  refracting  surfaces  has  a  Kryptok  lens  in  its 
reading  portion?  How  many  refracting  surfaces  to  the  distance 
part  of  the  lens? 

In  the  reading  portion  there  are  three  refracting  surfaces, 
the  two  outer  surfaces,  which  are  in  contact  with  the  air,  and  the 
inner  surface,  where  the  flint  fits  into  the  crown  glass. 


Practical  Optics  121 

The  distance  portion  has  the  usual  two  refracting  surfaces 
both  in  contact  with  air. 


On  what  principle  is  based  the  test  for  finding  the  optical 
center  of  a  le?is? 

At  the  small  portion  of  the  lens  occupied  by  the  optical 
center  the  surfaces  are  assumed  to  be  parallel  and  there  is  no 
bending  of  rays  of  light.  But  as  this  point  is  departed  from, 
curvature  comes  into  evidence  with  refractive  and  prismatic 
power,  increasing  from  the  center  to  the  periphery. 


Taking  a  +  1.50  D.  lens  from  the  trial  case,  what  other  lens 
must  be  added  to  it  to  produce  a  positive  focus  of  two  meters? 

A  focal  distance  of  two  meters,  or  eighty  inches,  is  produced 
by  a  +  .50  D.  lens;  hence  in  order  to  reduce  this  +  1.50  D.  lens 
to  such  power  we  must  add  —  ID. 


What  is  the  dioptric  power  of  a  lens  which,  being  decent ered 
5  mm..,  shows  a  prismatic  deviation  of  two  prism  diopters? 

The  rule  is  that  for  every  decentration  of  10  mm.  there 
are  as  many  diopters  of  prismatic  power  as  there  are  of  refractive 
power.  As  this  question  calls  for  a  decentration  of  5  mm.,  there 
would  be  half  as  many  prism  diopters  as  there  are  refractive 
diopters.  And  as  the  deviating  power  of  a  prism  is  equal  to  only 
one-half  of  its  refracting  angle,  there  would  be  only  one-fourth 
as  much  prismatic  deviation  as  there  are  diopters  of  refractive 
power. 

Therefore,  in  order  to  produce  a  deviation  of  2  prism  diopters, 
the  power  of  the  lens  must  be  8  D.,  which,  decentered  5  mm., 
would  show  4  diopters  of  prismatic  power  and  2  diopters  of 
deviation. 


On  what  particular  quality  of  the  glasses  used  does  the  optician 
depend  to  secure  the  necessary  reading  addition  in  fused  bifocals? 

On   the  fact   that   the  index   of  refraction   of   the   reading 
addition  is  so  much  higher  than  that  of  the  distance  glass,  that 


122  State  Board  Examinations 

with  the  same  curvature  on  each  the  former  would  show  a  much 
greater  refracti\e  power,  and  when  properly  figured  out  would 
afford  the  additional  power  desired  for  reading. 


What  curvature  must  be  given  to  the  two  surfaces  of  a  wafer  to 
produce  a  2.50  D.  reading  addition,  the  distance  correction  being 
-{-ID.  cylinder,  the  lenses  to  be  made  toric  on  a  -\-  6  D.  base? 

As  the  lens  is  a  plane  cylinder  and  the  base  curve  of  the 
toric  surface  is  to  be  +  6  D.,  the  inner  surface  must  be  ground 
—  6  D.  in  order  to  produce  neutralization  in  the  meridian  of  the 
axis  of  the  cylinder.  Therefore,  the  one  surface  of  the  wafer 
must  be  +  6  D.  in  order  to  fit  close  to  the  —  6  D.  surface,  and 
then  in  order  to  reduce  the  power  of  the  wafer  to  +  2.50  D.  its 
other  surface  must  be  —  3.50  D. 


Why  shoidd  the  optic  centers  of  a  pair  of  lenses  for  close  work 
be  2  to  3  mm.  nearer  together  than  the  optic  centers  of  lenses  for 
distant  vision? 

On  account  of  the  greater  convergence  of  the  visual  lines 
in  near  vision,  and  in  order  to  avoid  prismatic  effect. 


What  particidar  advantage  has  the  meniscus  form  of  lens  for 
bifocal  glasses? 

In  order  to  prevent  the  visual  lines  passing  obliquely  through 
the  lenses,  as  will  necessarily  be  the  case  with  fiat  lenses,  as  the 
eyes  turn  down  in  near  vision,  whereas  w4th  the  meniscus  form 
of  lenses  the  visual  lines  are  more  nearly  at  right  angles  to  the 
plane  of  the  glasses,  which  is  the  condition  to  be  desired  in  order  to 
avoid  anv  extra  cvlindrical  effect. 


Hoiv  can  you  find  the  principal  focal  length  in  inches  and  in 
millimeters  of  a  -\-  6  D.  lens? 

In  order  to  find  the  principal  focal  length  in  inches,  we  divide 
the  6  D.  into  40  inches,  and  the  result  is  approximately  6^ 
inches. 


Practical  Optics  123 

In  order  to  find  it  in  millimeters,  we  divide  the  6  D.  into  1,000 
millimeters,  and  the  result  is  approximately  166  mm. 


What  is  the  power  of  each  surface  of  a  scale  used  in  a  cement 
bifocal,  where  the  prescription  is  —  1  D.  sph.  =  -\-  1.25  D.  cyl.  axis 
180°,  and  +  1.75  for  reading? 

The  scale  would  be  cemented  on  the  concave  surface  of  this 
sphero-cylinder,  which,  being  —  1  D.,  would  call  for  +  1  D.  on 
one  surface  of  the  scale,  and  the  other  surface  +  .75  D.,  to  make 
up  the  desired  power.  

Why  is  it  necessary  to  locate  the  optical  center  of  a  lens  before 
edge  grinding  and  mounting? 

In  order  to  prevent  any  prismatic  effect  in  the  completed 
lens.  

In  u'hat  two  ways  is  the  strength  and  character  of  a  lens  found? 

By  the  lens  measure,  which  is  the  easiest  and  quickest  way, 
and  by  neutralization,  which,  while  more  troublesome,  is  more 
accurate.  

Hoiv  may  the  axis  of  a  cylindrical  lens  be  found? 

By  the  lens  measure,  or  by  finding  that  meridian  of  a  lens 
in  which  there  is  no  motion. 

Look  through  the  lens  at  a  straight  line  and  rotate  the  lens 
until  the  line  as  seen  through  and  beyond  the  lens  forms  one 
unbroken  line;  this  will  be  one  of  the  principal  meridians,  either 
that  of  greatest  refraction  or  of  no  refraction  at  all.  The  latter, 
being  the  axis,  could  be  determined  by  the  absence  of  motion. 


Suppose  we  wish  a  toric  lens  to  have  a  total  dioptric  power 
equal  to  -\-  1  Z^  +  .50  cyl.  axis  120°,  and  the  lens  measure  to  show 
the  power  of  one  surface  to  be  —  6  D.,  what  will  be  the  powers  of  the 
two  principal  meridians  of  the  toric  surface? 

This  can  be  easily  worked  out  diagrammatically.   The  first 
diagram  shows  the  power  of  each  of  the  meridians  of  the  sphero- 


124 


State  Board  Examinations 


cylinder,  and  the  second  diagram  the  complete  toric  lens,  from 
which  it  is  learned  that  the  powers  of  the  two  principal  me- 
ridians on  the  toric  surface  are  -f-  7  in  the  120th  meridian  and 
+  7.50  in  the  30th  meridian. 

A  toric  lens,  which  is  built  up  from  a  base  curve  of  6  D.  on  the 
toric  surface.  The  outside  surface  of  such  lens  would  show  a  +  6 
D.  curve  in  the  90th  meridian  and  a  +  7  D.  curve  in  the  180th 
meridian,  while  the  deep  concave  surface  towards  the  eye  would 
be  -  6  D. 


Fig.  23 


To  what  crossed  cylinder  from  the  trial  case  does  the  following 
correspond:  30th  meridian  +  3.25  D.,  and  120th  meridian 
+  4.25  D.? 

Inasmuch  as  axis  is  always  at  right  angles  to  meridian,  we 
have  +  3.25  D.  cyl.  axis  120°  C  +  4.25  D.  cyl.  axis  30°. 


In  what  way  does  crowft  glass  differ  from  flint  glass  as  to  disper- 
sion and  refractive  index? 

Crown  glass  has  a  lower  index  of  refraction  and  shows  less 
dispersion,  while  flint  glass  has  a  higher  index  of  refraction  and  a 
much  greater  power  of  dispersion. 

This  difference  in  dispersive  power  is  made  use  of  in  the  manu- 
facture of  achromatic  lenses,  where  the  convex  lens  is  made  of 
crown  glass  and  show^s  an  excess  of  refractive  over  dispersive 
power,  and  the  concave  lens  is  made  of  flint  glass  and  shows  an 
excess  of  dispersive  over  refractive  power.  This  relation  is  such 
that  the  concave  lens  corrects  the  dispersion  of  the  convex  lens 
without  neutralizing  all  of  its  refraction,  and  the  combination 
will  be  an  achromatic  lens,  which  is  refractive  but  not  dispersive. 


Practical  Optics  125 

In  prescribing  a  high  power  concave  lens,  how  can  the  weight 
of  glass  he  reduced  without  decreasing  the  size  of  lens? 

By  grinding  down  or  thinning  the  marginal  parts  of  the  lens, 
sometimes  called  "flattened  face,"  and  known  to  the  trade  as 
lenticular  lenses. 


How  can  the  axis  of  the  cylinder  in  a  compound  he  located  when 
the  sphere  is  high  and  the  cylinder  is  of  low  power? 

By  looking  through  a  pinhole  the  preponderance  of  the 
sphere  is  very  much  reduced  and  then  the  presence  of  the  cylinder 
soon  becomes  evident.  This  is  a  little  practical  point  that  is  not 
as  generally  known  as  it  should  be. 


What  is  decentered  lens  and  how  can  it  he  decentered? 

A  decentered  lens  is  one  in  which  the  optical  center  has  been 
moved  away  from  the  geometrical  center,  by  cutting  the  lens 
out  of  the  blank  to  one  side.  The  amount  of  decentering  depends 
upon  the  size  of  the  blank,  and  as  these  are  not  very  large  the 
limit  of  decentration  is  about  3  mm. 


Hew  is  the  optical  center  of  a  lens  found? 

Hold  the  lens  some  little  distance  from  the  eye  and  look 
through  it  at  a  straight  line,  moving  the  lens  until  the  line  is  con- 
tinuous above,  below  and  through  the  lens,  and  mark  the  same 
with  ink.  Turn  the  lens  around  and  repeat  the  same  procedure 
with  the  meridian  at  right  angles  to  the  first.  The  intersection  of 
the  two  lines  will  indicate  the  optical  center  of  the  lens. 


What  is  the  difference  in  the  nature  of  the  surface  of  a  sphero- 
cylinder  and  a  toric  lens  of  the  same  dioptric  power? 

In  a  sphero-cylinder  one  surface  is  ground  with  a  spherical 
curve  and  the  other  surface  with  a  cylindrical  curve.  In  a  toric 
lens  there  are  two  curvatures  on  one  surface,  thus  giving  the  effect 
of  a  sphero-cylinder  all  on  one  surface. 


126  State  Board  Examinations 

What  is  an  achromatic  lens,  and  does  it  correct  all  chromatic 
aberration? 

An  achromatic  lens  is  a  compound  lens  made  up  of  a  convex 
lens  of  crown  glass  with  an  excess  of  refractive  over  dispersive 
power,  and  a  concave  lens  of  flint  glass  with  an  excess  of  disper- 
sive over  refractive  power.  In  this  way  the  dispersion  is  over- 
come without  neutralizing  the  refraction,  and  the  combination 
will  be  a  refractive  but  not  a  dispersive  lens,  producing  a  white 
spot  free  from  colored  edges.  We  assume  it  corrects  the  chromatic 
aberration  and  so  it  does  for  all  practical  purposes,  but  as  all 
instruments  have  their  limitations,  it  may  fail  to  do  so  perfectly. 


What  is  the  purpose  of  bifocal  lenses,  and  why  are  they  some- 
times not  satisfactory? 

To  hold  before  the  eyes  for  immediate  use  the  two  pairs  of 
glasses  that  are  necessary  for  distant  and  near  vision  in  a  presby- 
opic ametrope. 

The  chief  reason  why  they  are  not  satisfactory  is  that  in  look- 
ing down  as  in  walking  or  stepping,  the  person  looks  through  the 
lower  part  of  the  lenses  which  are  fitted  for  reading  at  12  to  15 
inches,  whereas  the  ground  or  steps  are  at  a  distance  of  65  to 
70  inches. 


What  are  some  of  the  advantages  and  disadvantages  of  the 
use  of  Canada  balsam  in  bifocals? 

The  advantage  is  that  it  is  easy  to  use,  while  the  disadvan- 
tages are  that  it  does  not  become  perfectly  hard,  and  hence  when 
glasses  are  heated  or  vigorously  rubbed  the  wafers  are  apt  to  slip. 


A  segment  for  reading  is  attached  to  a  distance  lens  whose  power 
on  the  surface  to  which  the  segment  is  attached  is  minus  1.25.  The 
power  to  be  added  for  reading  is  plus  1.50;  what  will  be  the  power 
of  each  of  the  surfaces  of  the  segment? 

This  is  simply  the  attachment  of  a  segment  to  the  usual  form 
of  periscopic  convex  lens,  which  always  shows  on  its  inner  surface 
a  curvature  of  —  1.25  D.  As  this  is  the  surface  to  which  the  seg- 
ment should  be  attached,  the  latter  must  have  a  corresponding 


Practical  Optics  127 

convex  curve,  which  would  be  +  1-25  D.  on  one  surface.  To  get 
the  total  power  of  +  1.50  D.  which  it  is  desired  to  add  for  reading, 
the  extra  power  needed  over  the  +  1.25  D.  will  be  +  .25  D.,  which 
will  be  the  power  of  the  other  surface.  Hence  the  segment  will  be 
+  1.25  D.  on  one  surface  and  +  .25  D.  on  the  other. 


What  effect  is  produced  hy  the  decentration  of  a  lens? 

A  prismatic  effect,  the  amount  of  which  depends  upon  the 
extent  of  the  decentration,  and  the  curvature  of  the  lens,  in  the 
proportion  of  1°  of  prismatic  power  for  every  diopter  of  refraction 
power,  when  decentered  10  mm. 


What  constitutes  the  axis  of  a  cylindrical  lens,  and  how  is  it 
found  and  numbered? 

That  meridian  of  the  lens  which  is  piano  or  without  curva- 
ture constitutes  the  axis  of  the  cylinder.  In  a  piano-cylindrical 
lens  it  coincides  with  that  meridian  in  which  there  is  no  motion. 
Or  it  may  be  found  by"  looking  through  the  lens  at  a  straight 
line  and  rotating  it  to  that  position  where  the  line  is  continuous 
and  unbroken,  and  which  will  indicate  the  position  of  one  of 
the  principal  meridians,  the  other  principal  meridian  will  be 
exactly  at  right  angles,  one  of  which  will  be  the  axis  as  indicated 
by  the  absence  of  motion. 

How  should  glasses  be  adjusted  so  as  to  serve  for  both  distance 
and  reading? 

It  is  impossible  to  adjust  glasses  so  that  they  will  be  accu- 
rately centered  both  for  distance  and  reading,  as  the  centers  of 
reading  glasses  should  be  closer  and  lower  than  those  for  distance. 
The  only  thing  that  can  be  done  is  to  strike  a  compromise,  and 
when  the  same  glasses  are  used  for  both  purposes  to  make  the 
centers  slightly  lower  and  slightly  closer  than  would  be  proper 
for  distance,  but  not  so  low  or  so  close  as  would  be  desirable  for 
reading  alone. 

Write  a  prescription  that  shall  contain  a  cylindric  element 
for  both  eyes,  with  a  difference  in  the  spheric  element  of  at  least 


128  State  Board  Examinations 

2  D.  and  with  a  presbyopic  addition  of  1 .75  for  each  eye  The  lenses 
are  to  Iw  made  in  cemented  bifocal  form.  State  what  decentration 
is  necessary  in  order  that  there  shall  be  no  resulting  imbalance  when 
the  wearer  is  looking  through  the  reading  portion  of  the  lens. 

We  will  write  supposed  prescription  as  follows: 

R.  +  1-50  P.  S.  o  +  .50  P.  cyl.  axis  90° 
+  1.75  P.  added 

L.  +  3.50  P.  S.  o  +  .50  P.  cyl.  axis  90° 
+  1.75  added 

As  the  pupillary  distance  for  reading  is  4  mm.  less  than  for 
distance,  there  is  produced  in  reading  vision  a  decentration  of 
2  mm.  outward  for  each  eye,  which  for  the  2  D.  value  in  the 
distance  lens  of  right  eye  is  equivalent  to  .4°. 

For  the  left  eye  under  the  same  conditions  the  4  D.  of 
refractive  power  would  aflbrd  a  prismatic  power  of  .8°. 

The  segment  must  be  decentered  inwards  in  order  to  neutral- 
ize the  prismatic  effect  of  the  distance  lens.  If  a  +  1.75  D.  lens 
decentered  10  mm.  produces  1.75°  prismatic  power,  in  order  to 
get  .4°  the  problem  would  be 

1.75  :  10  :  :  .4  :  X 

X=    -;-  =  2.29  „.n.. 

And  as  the  segment  must  be  decentered  inwards  2  mm. 
anyhow,  the  total  decentration  of  segment  for  right  eye  would 
be  4.29  mm. 

As  the  distance  lens  for  left  eye  is  twice  as  strong,  the  amount 
of  decentering  of  segment  to  overcome  it  would  be  4.58  mm., 
which  added  to  the  customary  decentering  of  2  mm.,  would 
make  a  total  decentering  of  left  segment  6.58  mm. 

Which  side  of  a  toric  lens  is  the  base  curve,  the  inner  or  outer? 

The  base  curve  is  the  least  curve  on  the  toric  surface,  and 
as  this  is  usually  on  the  convex  surface  the  base  curve  is  mostly 
out.  But  the  base  curve  may  be  on  the  concave  surface  and  then 
it  is  in. 


//  a  spherical  lens  has  a  deep  concave  curvature  on  one  side, 
is  it  a  toric  sphere  or  a  meniscus? 


Practical  Optics  129 

The  word  toric  implies  two  curvatures  on  the  same  surface, 
and  therefore  strictly  speaking  a  sphere  cannot  be  a  toric. 
But,  on  account  of  the  deep  concave  curve  that  is  usually  ground 
on  toric  lenses,  the  term  has  come  to  be  applied  to  all  lenses 
showing  such  a  curve  even  though  they  be  spheres;  therefore,  a 
toric  sphere  and  a  meniscus  are  practically  the  same  thing. 


Explain  the  construction  of  the  spherometer  and  state  its 
limitations. 

The  spherometer,  or  lens  measure,  has  three  projecting  metal 
pins,  the  two  outside  ones  fixed  and  the  central  one  projecting 
beyond  the  other  two,  movable  and  connected  with  a  spring, 
which  controls  the  pointer  on  the  dial  which  indicates  the 
dioptric  number  of  the  lens.  When  used  on  a  lens  the  central 
pin  is  depressed  and  causes  the  pointer  to  revolve  and  indicate 
the  power  of  the  lens. 

The  limitations  of  the  instrument  are  that  it  measures  only 
the  curvature  of  the  surface,  and  takes  no  account  of  the  index 
of  refraction  of  the  glass  of  which  the  lens  is  made.  If  all  glass 
was  made  of  the  same  index  of  refraction  the  lens  measure  would 
always  be  correct.  But,  inasmuch  as  the  index  varies,  it  would 
be  correct  for  only  one  particular  index,  and  incorrect  for  lenses 
of  other  indices. 


//  a  hypermetrope  is  wearing  a  pair  of  -\-  4  D.  sph.,  and  these 
are  by  mistake  decentered  outward  6  mm.  each,  what  is  the  amount 
of  prismatic  effect  produced,  and  which  direction  are  the  bases? 

On  the  basis  of  1°  for  each  dioptric  when  decentered  10  mm., 
the  effect  in  this  case  would  be  2.4°  for  each  eye  bases  outwards. 


The  letis  measure  shows  the  inner  surface  of  a  toric  lens  to 
be  —  4  D.  sphere  and  the  outer  surface  a  +  6  D.in  the  90th  meridian, 
+  8.25  D.  in  the  180th  meridian;  what  is  the  power  of  the  lens,  and 
what  is  its  base  curve? 

The  base  curve  would  be  +  6  D.  and  the  value  of  the  lens 
+  2  D.  S.  C  +  2.25  D.  cyl.  axis  90°. 


130 


State  Board  Examinations 


What  lens  can  be  combined  with  a  -\-  2  D.  S.  C^  -\-  1  D.  cyl. 
axis  90°  that  will  decrease  the  cylinder  and  increase  the  sphere? 

If  a  cylinder  is  placed  at  right  angles  then  the  power  of  both 
sphere  and  cylinder  is  changed;  if  the  added  cylinder  be  concave 
the  sphere  is  decreased  and  the  cylinder  increased.  If  the  added 
cylinder  be  convex  the  sphere  is  increased  and  the  cylinder 
decreased. 

Suppose,  for  example,  we  add  +  .25  D.  cyl.  axis  180°  to 
the  given  formula,  then  we  have  +  2  D.  S.  O  +  1  D.  cyl.  axis 
90°  C   +  .25  D.  cyl.  axis  180°. 

By  the  rules  of  transposition  this  is  equivalent  to  +  2.25 
D.  S.  C   +  .75  D.  cyl.  axis  90°. 


What  lens  can  be  combined  with  the  above  that  will  increase 
the  cylinder  and  decrease  the  sphere? 

A  concave  cylinder  with  axis  at  right  angles.  Suppose  we 
add  —  .25  D.  cyl.  axis  180°  to  the  given  formula,  as  follows: 
+  2  D.  S.  C  +  1  D.  cyl.  axis  90°  C  -  -25  D.  cyl.  axis  180°. 

Transposing  this  cross  cylinder  and  adding  the  sphere,  we 
have  +  1.75  D.  S.  C  +  1.25  D.  cyl.  axis  90°. 


If  you  had  a  case  calling  for  +  1.25  D.  S.  C^  +  0.75  D.  cyl. 
axis  90°,  and  the  lenses  were  to  be  torics  with  minus  6  D.  curve  next 
to  the  eye,  what  would  be  the  curves  on  the  outside  of  the  lens? 

The  best  way  is  to  make  a  cross  showing  the  value  in  each 
meridian,  to  which  the  toric  transposition  must  be  made  to 
conform. 


+  1.25 


+  1.25 

+    .75 

+  2.00 

Sphero-cylindrical  Values 


-  6. 

+  7.25 


+  1.25 


-  6. 

+  8. 

+  2. 


Toric  Curves  and  Values 


Practical  Optics  131 

In  order  to  maintain  the  powers  of  the  sphero-cylinder,  the 
curvatures  of  the  outer  surface  would  be  +  7.25  vertically  and 
+  8  horizontally. 

This  would  mean  a  base  curve  of  +  7.25,  but  as  a  matter  of 
fact  the  base  curve  is  usually  6  D.  on  the  toric  surface,  instead 
of  6  D.  on  the  spherical  surface. 


A  sphero-cylindrical  lens  has  its  axis  set  at  some  unknown 
angle;  hoiv  would  you  ascertain  at  ivhat  angle  the  meridian  of 
greatest  refraction  is  placed?  At  what  angle  is  the  meridian  of  least 
refraction?  Are  these  two  angles  ahvays  to  he  found  at  right  angles 
to  one  another?    If  they  are,  explain  why;  and  if  not,  why  not? 

In  a  sphero-cylindrical  lens  there  are  two  chief  meridians  to 
be  considered ;  one  of  least  refraction  and  one  of  greatest  refrac- 
tion. In  order  to  ascertain  the  location  of  these  meridians,  a 
straight  vertical  line  should  be  looked  at  through  the  lens;  the 
edge  of  a  window  sash  or  a  picture  frame  will  answer.  The  lens 
should  be  held  some  distance  from  the  eye  and  as  it  is  rotated  the 
part  of  the  line  that  is  seen  through  the  lens  will  break  away  from 
that  part  of  the  line  seen  above  and  below  the  lens,  and  then 
come  back  to  its  original  position. 

The  lens  is  rotated  to  that  point  where  the  line  is  continuous 
above,  below  and  through  the  lens,  and  this  will  represent  one  of 
the  chief  meridians  of  the  lens,  and  the  other  meridian  will  be 
exactly  at  right  angles  to  it.  The  lens  is  then  moved  along  these 
two  meridians,  when  the  meridian  of  greatest  refraction  is  that  in 
which  the  movement  is  the  most  decided,  and  the  meridian  of 
least  refraction  that  in  which  the  movement  is  least  noticeable. 

The  meridians  of  least  and  greatest  refraction  are  necessarily 
at  right  angles  to  each  other  on  accountof  the  natureof  the  curves, 
the  former  corresponding  to  the  axis  of  the  cylinder  where  the 
power  is  that  of  the  sphere  alone,  and  the  latter  at  right  angles  to 
the  axis  where  the  power  is  equal  to  that  of  the  sphere  and  cylinder 
combined. 

Describe  very  carefully  what  will  he  seen  on  looking  at  a  hori- 
zontal window  har  against  the  bright  sky  through  a  thin  prism  held 
with  its  base  upwards. 


132  State  Board  Examinations 

Thar  part  of  the  bar  seen  through  the  prism  will  be  displaced 
downwards  or  in  the  direction  of  the  apex  of  the  prism. 

Prisms  cause  dispersion  of  light,  but  this  will  scarcely  be 
noticeable  in  an  experiment  like  this. 


A  person,  aged  sixty,  brings  you  the  followitig  prescription  for 
distant  vision: 

R.  E.  -  2  D.  sphere  C  +  1.50  D.  cyl.  axis  90° 
L.  E.  -  ID.  sphere  C  +  .75  D.  cyl.  axis  90° 
Can  you  improve  on  this  prescription  without  altering  the  poiver? 
What  glasses  would  you  give  him  for  reading  at  14"? 

This  prescription  can  be  transposed  into 

R.  E.  -  .50  D.  S.  C  -  1.50  D.  cyl.  axis  180° 
L.  E.  -  .25  D.  S.  C  -  .75  D.  cyl.  axis  180° 
But  this  transposition  does  not  present  any  advantages  over 
the  original  because  although  they  might  be  lighter,  the  periscopic 
efifect  would  be  lost.  For  this  reason  we  would  choose  the  former, 
and  also  because  of  the  vertical  position  of  the  axis  of  the  cylinders, 
which  is  preferable. 

At  the  age  of  60  the  amplitude  of  accommodation  of  the 
average  eye  is  about  1  D.,  of  which  the  person  can  use  one-half 
for  near  work.  In  order  to  read  at  14  inches  without  accommo- 
dation, a  lens  of  +  2.75  is  called  for,  but  as  this  patient  can  supply 
.50  D.  of  accommodation,  the  presbyopic  addition  would  be 
theoretically  +  2.25,  but  as  a  matter  of  fact  and  judging  from 
experience  we  would  say  that  it  ought  to  be  at  least  +  2.50  D. 
If  we  add  these  to  the  first  formula  we  have 

R.  E.  +     .50  D.  S.  C  +  1.50  D.  cyl.  axis  90° 
L.  E.  +  1.50  D.  S.  C   +     .75  D.  cvl.  axis  90° 
If  we  add  to  the  second  formula  we  have 

R.  E.  +  2.00  D.  S.  C   -  1.50  D.  cyl.  axis  180° 
L.  E.  +  2.25  D.  S.  C   -     .75  D.  cyl.  axis  180° 
As   the  second   form   gives   periscopic  shaped   lenses,    they 
should  be  given  the  preference. 

How  would  you  determine  the  focal  length  of  a  simple  bi-convex 
lens  with  surfaces  of  equal  curvature?  Give  all  the  practical  methods 
you  know  of. 


Practical  Optics  133 

1.  By  neutralization  with  a  concave  lens. 

2.  By  allowing  rays  of  light  from  an  object  at  least  20  feet 
away  to  pass  through  the  lens  and  form  an  image  on  a  screen, 
moving  the  lens  closer  to  and  farther  from  screen  until  the  point 
is  found  where  image  is  most  distinct,  and  then  measuring  the 
distance  from  the  lens  to  the  screen. 

3.  By  measurement  of  the  curvature  of  each  surface  by  the 
lens  measure. 

4.  If  the  radius  of  curvature  was  known  and  the  index  of 
refraction  of  the  glass  from  which  the  lens  is  made,  we  can  find 
the  focal  distance  by  the  following  rule:  divide  the  radius  of 
curvature  by  twice  the  index  of  refraction  less  one,  and  the  result 
will  be  the  focal  distance. 

What  is  the  composition  of  flint,  crown  and  window  glass? 
What  are  pebble  lenses? 

The  composition  of  flint  glass  is  as  follows: 

Silica 50  parts 

Lead 30      " 

Potash 10      " 

Other  ingredients 10 

100  parts 
And  crown  glass: 

Silica 70  parts 

Soda 10      " 

Lime :....    10      " 

Other  ingredients 10 


100  parts 
Window  glass  is  similar  in  composition  to  crown  glass,  but 

not  quite  so  good  quality. 

Rock  crystal  or  quartz  is  a  product  of  Nature,  and  when  cut 

into  a  slab  or  ground  to  form  a  lens  is  called  a  pebble. 

Pebble  lenses  should  be  clear  and  free  from  striae,  specks  and 

flaws  and  should  be  axis  cut. 


A  prescription  calls  for  -{-  1  O  +  50  X  135  in  toric  lenses, 
minus  6  base  curve.  Whit  will  the  lens  measure  show  on  two 
surfaces? 


1 34  State  Board  Examinations 

On  the  concave  surface  towards  the  eye  —  6  D.  in  the  45th 
meridian  and  —  6.50  D.  in  the  135th  meridian;  on  the  convex 
surface  +  7.50  in  all  meridians. 


Sphero  cylinders  have  two  focal  lines.  What  must  be  the 
condition  so  that  these  lines  will  have  an  actual  existence? 

The  sphero  cylinder  must  be  convex  and  then  rays  of  light 
passing  through  it  will  be  made  to  meet  at  the  focal  distances  of 
the  two  principal  meridians  in  the  form  of  focal  lines. 


What  is  the  character  of  the  two  focal  lines  in  a  piano  cylinder? 

In  the  meridian  of  the  axis,  the  surface  of  the  lens  is  piano 
and  there  would  be  no  action  on  light.  In  the  meridian  at  right 
angles  to  the  axis  the  rays  would  be  refracted  to  a  focal  line  at 
the  principal  focal  distance  of  this  meridian,  the  line  being  in 
the  same  direction  as  the  axis. 


The  following  glass  is  called  for:  +  4.5  sph.  C^  —  3  cyl.  axis 
45°.  What  will  the  measurements  be  if  this  is  made  up  as  a  toric 
on  a  6 -base  curve?  , 

This  will  depend  upon  whether  it  is  desired  to  have  the 
6  D.  base  curve  on  the  concave  or  the  convex  surface. 

If  the  base  curve  is  convex  we  would  have  +  6  D.  in  the 
135th  meridian  and  +  9  D.  in  the  45th  meridian,  and  the  inner 
surface  a  —  4.50  D.  curve. 

If  the  base  curve  is  concave,  —  6  D.  in  the  45th  meridian 
and  —  9  D.  in  the  135th  meridian,  and  the  outer  surface  a  + 
10.50  D.  curve. 


What  is  the  effect  produced  by  decentering  and  what  is  the  rule 
governing  the  same? 

When  a  ray  of  light  passes  through  the  peripheral  portion 
of  a  lens  it  is  bent  the  same  as  if  a  prism  was  used,  the  prismatic 
effect  increasing  with  the  distance  from  the  optical  center. 


Practical  Optics  135 

To  produce  the  effect  of  a  prism  with  its  base  in  a  certain 
direction,  a  convex  lens  is  decentered  in  that  same  direction  and 
a  concave  lens  in  the  opposite  direction.  For  example  to  assist 
convergence  a  convex  lens  is  decentered  in  towards  nose  and  a 
concave  lens  decentered  out  towards  temple. 

The  amount  of  prismatic  power  that  may  be  developed  by 
decentering  of  a  lens,  depends  upon  its  strength  and  the  amount 
of  decentering,  and  this  can  be  best  illustrated  by  the  prism 
diopter  system  of  numbering. 

Since  a  +  1  D.  lens  decentered  1  cm.  produces  a  prismatic 
power  of  1  A  ; 

And  if    P    represents  the  prismatic  power  desired,   D  the 

dioptric  power  of  the  lens,  and  C  the  decentration  in  centimeters; 

p 
then  P  =  DX   CorC  =  j^ 

For  example  if  a  +  4  D.  lens  be  decentered  5  cm.,  then 

p  =  4  X  5  =  2.0  A 
Or  if  the  effect  of  1  A  is  desired  with  a  +  5  D  lens,  the 
amount  of  decentration  would  be 

C  =  X  cm.  or  2  mm. 


What  is  a  mobile  or  rotary  prism? 

When  two  prisms  are  placed  in  apposition,  with  base  of 
one  to  the  apex  of  the  other,  there  will  be  neutralization  if  they 
are  of  equal  strength.  If  these  prisms  are  kept  in  apposition  and 
revolved  in  opposite  directions,  they  will  produce  the  effect  of 
a  single  prism,  gradually  increasing  in  strength  until  the  bases 
of  the  two  prisms  come  together,  when  the  effect  will  be  equal 
to  the  combined  strength  of  the  two  prisms,  as  was  first  pointed 
out  by  Sir  John  Herschel,  an  illustrious  English  astronomer,  who 
died  in  1871. 

'  The  rotary  prism  consists  of  two  superimposed  prisms  of 
15°  each,  mounted  in  a  cell  of  the  size  of  a  trial  lens.  By  means 
of  a  milled-head  screw  these  prisms  are  made  to  revolve  against 
each  other.  When  the  base  of  one  lies  over  the  apex  of  the 
other,  there  is  neutralization,  and  the  indicator  points  to  zero. 
As  the  screw  is  turned  and  the  prisms  begin  to  rotate,  prismatic 
power  is  developed  as  shown  by  the  indicator,  2°,  4°,  6°  up  to  30°, 


136  State  Board  Examinations 

the  full  power  being  reached  when  the  bases  of  the  two  prisms 
are  in  apposition. 

This  rotary  prism  can  be  used  in  a  trial  frame  and  can  be 
placed  so  as  to  present  the  base  of  the  increasing  prism  up  or 
down,  in  or  out. 


Give  all  the  curves  of  a  bifocal  lens,  the  distance  lens  being 
2  D.  S.  Z^  —ID.  cyl.  90°  and  the  power  of  the  segment  being  + 
2  D.  What  difference  wotdd  there  be  if  the  index  of  refraction  of 
the  glass  used  was  1.50  and  1.60  respectively? 

The  curvature  of  the  two  surfaces  of  the  distance  lens  would 
be  as  shown  by  the  formula.  The  segment  would  be  attached 
to  the  spherical  surface,  and  would  show  a  —  2  D.  curve  on  the 
inside  and  a  +  4  D.  curve  on  the  outside. 

When  w'e  say  a  —  2  D.  curve  or  a  +  4  D.  curve  we  usually 
mean  a  curve  that  will  produce  —  2D.  power  or  that  will  show 
+  4  D.  power;  but  as  a  matter  of  fact,  in  order  to  produce  —  2D. 
power,  the  radius  of  curvature  must  be  10  inches;  and  in  order 
to  produce  +  4  D.  power,  the  radius  of  curvature  must  be  5 
inches,  or  in  other  words,  the  focus  is  twice  the  radius. 

The  above  figures  apply  only  in  case  the  irrdex  of  refraction 
of  the  glass  is  1.50.  If  the  glass  used  had  an  index  of  refraction 
of  1.60,  then  the  radius  of  curvature  necessary  to  produce  +  4  D. 
power  would  be  5.45  inches. 

The  standard  formula  to  find  the  focal  length  of  a  lens  is  as 

follows : 

.-■-I 
F  = 


(r    +    r^)    (u    -    1) 

Substituting  figures  of  the  above  case 

10  r  -  lOr 


20  = 


(-    10    +    r)    .6         -    6.    +    .6r 


Clearing  of  fractions  we  have 

-  120  +  12  r  =   -  lOr 

-  120  =   -  22  r 

r  =   +  5.45  inches. 


Theoretic  Optometry 

An  anisometrope  wears  on  the  right  eye  a  -]-  2  and  on  the 
left  eye  a  —  2;  his  glasses  are  centered  properly  for  distance;  what 
is  the  nature  of  the  prismatic  action  of  the  lenses  when  he  looks  at 
a  nearby  object? 

As  convergence  comes  into  play  and  he  looks  at  a  near 
object  the  visual  lines  pass  in  each  lens  slightly  to  the  inner  side 
of  the  optical  center. 

For  the  right  eye  as  he  looks  through  a  convex  lens  inside 
of  its  center,  the  prismatic  efifect  produced  is  that  of  base  out. 
For  the  left  eye  looking  through  a  concave  lens  at  its  inner  side, 
the  effect  is  prism  base  in.  As  the  lenses  are  of  the  same  strength 
the  prismatic  efifect  produced  will  be  equal  in  each  eye,  and  one 
will  neutralize  the  other. 


Name  and  describe  eight  subdivisions  of  heterophoria.     Draw 
a  diagram  illustrative  of  each  condition. 

Exophoria,  in  which  there  is  a  tendency  to  deviation  outward, 
and  the  test  shows  the  image  of  right  eye  to  the  left. 


Fig.  24 


Esophoria,  in  which  there  is  a  tendency  to  deviation  inward, 
and  the  test  shows  the  image  of  right  eye  to  the  right. 


Fig.  25 


Right  Hyperphoria,  in  which  there  is  a  tendency  for  the  right 
visual  line  to  deviate  above  the  left.  The  test  shows  the  image 
of  right  eye  to  be  below  the  left.      (See  Fig.  26,  page  138.) 


137 


138  State  Board  Examinations 

Left  Hyperphoria,  in  which  there  is  a  tendency  for  the  left 
visual  line  to  deviate  above  the  right.  The  test  shows  the  image 
of  right  eye  to  be  above  the  left.      (See  Fig.  27  below.) 


Fig.  26  Fig.  27 


Right  Hyperexophoria,  in  which  there  is  a  tendency  for  the 
right  visual  line  to  deviate  upwards  and  outwards. 

The  test  shows  the  image  of  right  eye  to  be  below  and  to 
the  left. 


Fig.  28 


Right  Hyperesophoria,  signifying  a  tendency  for  the  right 
visual  line  upward  and  inward.  The  test  shows  the  image  of 
the  right  eye  to  be  below  and  to  the  right. 


Fig.  29 


Left  Hyperexophoria,  a  tendency  of  the  left  visual  line  upward 
and  outward.  The  test  shows  the  image  of  right  eye  above  and 
to  the  left. 

R 


Fig.  30 


Theoretic  Optometry  139 

Left  Hyperesophoria,  a  tendency  of  the  left  visual  line  upward 
and  inward.  The  test  shows  image  of  right  eye  to  be  above  and 
to  the  right. 


Fig.  31 

Explain  how  an  eye  can  have  normal  visual  acuity  and  be 
ametropic. 

In  hypermetropia  and  hypermetropic  astigmatism,  if  of 
not  too  high  degree  and  in  young  persons,  the  action  of  the 
accommodation  would  neutralize  the  deficiency  of  refractive 
power  or  axial  length,  and  maintain  the  acuteness  of  vision  at 
the  normal  standard.  This  imposes  an  unnatural  tax  upon  the 
ciliary  muscle  and  leads  to  asthenopia. 


Is  there  any  advantage  in  correcting  an  ametropia  ivhen  visual 
acuity  is  normal? 

Yes,  in  order  to  lessen  the  unnatural  strain  upon  the  accom- 
modation, and  relieve  the  headache  and  other  symptoms  of 
asthenopia  which  are  otherwise  likely  to  occur. 


Why  is  it  desirable  to  know  the  far  and  the  near  point  of  vision? 

The  far  point  in  emmetropia  is  at  infinity,  in  hypermetropia 
beyond  infinity,  and  in  myopia  at  a  certain  finite  distance;  hence 
a  knowledge  of  the  far  point  indicates  the  character  of  the  refrac- 
tion. 

The.  position  of  the  near  point  represents  the  amplitude  of 
accommodation,  and  indirectly  by  comparison  with  the  normal 
standard  at  the  particular  age  shows  approximately  the  condition 
of  the  refraction.  In  hypermetropia  and  presbyopia  the  near 
point  is  of  importance  as  showing  the  impairment  of  accom- 
modation and  the  necessary  help  that  must  be  afforded  bv  convex 
lenses. 


140  Stale  Board  Examinations 

What  is  the  relation,  if  any,  of  heterophoria  to  heterotropia? 
Explain  fully. 

Heterophoria  is  a  tendency  to  a  departure  from  the  normal 
paralleHsm  of  the  visual  lines,  while  heterotropia  is  an.  actual 
deviation.  Heterophoria  is  a  latent  strabismus,  while  hetero- 
tropia is  a  manifest  condition. 


What  influence,  if  any,  has  the  correcting  of  errors  of  refraction 
on  muscular  deficiencies? 

When  esophoria  occurs  in  connection  with  hypermetropia, 
and  exophoria  with  myopia,  the  convex  lenses  in  the  first  case 
tend  to  correct  the  esophoria,  and  the  concave  lenses  in  the  second 
case,  the  exophoria. 

When,  however,  esophoria  is  found  in  connection  with 
myopia  and  exophoria  with  hypermetropia,  which  is  contrary 
to  the  usual  relation,  then  the  convex  lenses  needed  to  correct 
the  hypermetropia  would  aggravate  the  exophoria,  and  the 
concave  lenses  in  myopia  would  act  similarly  on  the  esophoria. 


What  muscles  are  taxed  in  (a)  abduction,  (b)  adduction, 
(c)  sursumduction?    Explain  fully . 

Abduction  is  accomplished  mainly  by  the  action  of  the 
external  recti  muscles,  which  is,  however,  reinforced  later  by 
the  two  obliques.  Hence  we  would  say  it  is  the  external  rectus 
that  is  taxed. 

Adduction  is  accomplished  mainly  by  the  action  of  the  in- 
ternal recti  muscles,  reinforced  later  in  the  act  by  the  superior 
and  inferior  recti.  We  would  say  it  is  the  internal  rectus  that  is 
taxed. 

In  sursumduction  the  vertical  muscles  are  taxed,  the  superior 
rectus  and  inferior  oblique  of  one  eye  being  antagonized  by  the 
inferior  rectus  and  superior  oblique  of  the  other. 


The  centers  of  a  pair  of  —  3.25  D.  spheric  lenses  mounted 
in  spectacles  are  found  to  be  2  mm.  farther  apart  than  the  pupillary 
centers  of  the  wearer;  what  prismatic  correction  has  he  been  wearing? 


Theoretic  Optometry  141 

The  rule  is  that  for  every  decentration  of  10  mm.  there 
will  be  as  many  degrees  of  prismatic  power  developed  as  there 
are  diopters  of  refractive  power  in  the  lens.  Therefore,  a  decen- 
tration of  a  3.25  spherical  lens  10  mm.  would  make  a  prismatic 
eflfect  of  3.25. 

Now  as  the  pupillary  distance  of  the  spectacles  is  2  mm. 
farther  apart  than  should  be  there  is  a  decentration  of  1  mm. 
for  each  eye,  representing  a  prism  of  0.325°  for  each  lens,  and  as 
it  is  a  concave  lens  and  the  decentration  is  outward,  the  base 
of  the  prism  is  in.  This  is  less  than  one-third  of  a  degree  for 
each  eye,  

An  eyeglass  mounting  containing  the  lens  correction, 

Right- 5. 00  D.  cyl.  X  180° 

Left- 3.00  D.  cyl.  X  180° 
has  become  bent  in  such  a  manner  that  the  wearer  is  looking  through 
the  right  lens  3  mm.  above  the  center  and  through  the  left  lens  2  mm. 
below  the  center;  what  is  the  resulting  imbalance  expressed  in  prism 
diopters? 

A  cylinder  if  decentered  in  the  direction  of  its  axis  would 
show  no  prismatic  power,  but  in  the  direction  at  right  angles 
to  its  axis  the  same  prismatic  value  as  a  sphere  of  similar  strength. 
Therefore,  in  this  case  we  have  a  —  5  D.  sphere  decentered  down- 
wards 3  mm.,  and  a  —  3  D.  decentered  upwards  2  mm.  with  the 
resulting  prismatic  values  as  follows: 

O.  D.  1>^  A  base  up 

O.  S.    3/5i  A  base  down 
or  a  total  prismatic  power  of  a  little  over  2  A. 


In  which  position  should  the  apex  of  the  prism  be  placed  to 
tax  the  strength  of  the  external  rectus  muscle? 

The  apex  of  a  prism  calls  a  muscle  into  action  and  taxes 
its  strength;  therefore  in  this  case  the  apex  should  be  out. 


Explain  the  cause  of  separation  of  the  corneal  images  of  the 
keratometer    targets. 

If  the  mires  are  placed  in  the  meridian  of  greatest  refraction 
so  that  the  reflected  images  are  just  in  contact,  there  will  be  a 


142  State  Board  Examinations 

separation   when   the  uistrunient  is  turned   to   the  meridian  of 
least  curvature. 


What  significance  may  be  attached  to  an  improvement  in 
vision  that  is  obtained  by  the  pin-hole  disk? 

If  impaired  vision  is  due  to  opacities  or  diseased  conditions, 
no  improvement  follows  the  use  of  the  pin-hole  disk  or  any 
other  test.  But  if  improvement  in  vision  is  afforded  by  the  pin 
hole,  the  impaired  vision  is  shown  to  be  due  to  refractive  error 
and  imperfect  focusing  upon  the  retina  and  we  can  expect  an 
equal  improvement  from  lenses. 


For  what  purpose  is  the  double  prism  found  in  some  trial 
cases  used,  and  ho%u  is  it  used? 

It  is  one  of  the  tests  for  muscle  imbalance. 

It  is  placed  over  one  eye  while  the  patient  looks  at  the  light. 
Care  must  be  taken  that  the  line  of  separation  between  the  two 
prisms  is  directly  in  the  line  of  vision,  in  which  case  two  lights 
will  be  seen  by  this  eye,  one  above  the  other. 

When  the  other  eye  is  uncovered  a  third  light  will  be  seen, 
the  position  of  which  will  show  if  any  heterophoria  is  present,  and 
its  character.  If  midway  between  the  two  images  and  in  the 
same  vertical  line,  there  is  no  imbalance. 

If  the  middle  image  deviates  to  the  same  side  esophoria  is 
present;  if  to  the  opposite  side,  exophoria.  If  it  moves  up, 
hyperphoria  of  the  other  eye;  if  it  moves  down,  hyperphoria  of 
this  eye. 

For  the  detection  of  insufficiencies  of  the  oblique  muscles 
the  patient  looks  at  a  straight  line,  which  is  doubled  by  the 
prism,  the  two  lines  being  parallel  to  each  other.  When  the 
other  eye  is  uncovered  a  third  line  will  be  seen  between  the 
two  and  should  be  parallel  with  them.  If  this  middle  line  tilts 
in  either  direction  cyclophoria  is  shown. 


Looking  at  a  small  object  which  is  4  meters  distant  to  what 
extent  will  that  object  seem  to  be  displaced  if  a  prism  of  a  power  of 
4  prism  diopters  is  placed  before  the  eye?    Explain  the  reasoning. 


Theoretic  Optometry  143 

A  prism  diopter  deviates  a  ray  of  light  1  cm.  for  each  meter 
of  distance.  Hence  the  deviation  at  4  meters  would  be  4  cm. 
and  if  the  prism  was  4  A  the  deviation  would  be  16  cm.,  which 
is  the  answer. 


What  is  the  size  of  an  object  5  meters  away  that  forms  on  the 
retina  of  a  hyperope  of  3  D.  an  image  5  mm.  in  diameter? 

The  proportion  would  be  as  follows:  As  5000  mm.  is  to  the 
size  of  the  object,  so  is  14  mm.  to  5  mm.  To  make  the  calculation 
the  distance  of  the  object  must  be  multiplied  by  the  size  of  the 
retinal  image,  and  the  quantity  obtained  divided  by  the  distance 
of  the  nodal  point  from  the  retina. 

5000  mm.  X  5  mm. 


14  mm. 

—     =1/86  mm. 

The  completed  proportion 

would  be 

Size  Imaje                   Size  Object 

Distance 
No  lal  Point 

Distance  Objec 

5  mm.          :         1786  mm.          :     : 

14  mm.          : 

5000  mm. 

What  direction  must  rays  of  light  take  in  entering  a  hyperopic 
eye  to  focus  on  the  retina? 

With  the  accommodation  at  rest  the  rays  must  be  convergent 
in  order  to  focus  upon  the  retina  of  the  hypermetropic  eye;  and 
they  are  made  so  by  the  action  of  the  convex  lens  that  is  placed 
before  the  eye  to  correct  its  defect. 


What  direction  must  rays  of  light  take  in  entering  a  myopic 
eye  to  be  focused  on  the  retina? 

The  rays  of  light  must  be  divergent  in  order  to  focus  upon 
the  retina  of  the  myopic  eye,  and  they  are  made  so  by  the  action 
of  the  concave  lens  placed  in  front  of  the  eye  to  correct  its  defect. 


A  young  hyperope,  having  normal  acuteness  of  vision,  either 
with  or  without  +  .50  D.  spheric  lenses,  being  subjected  to  the 
dynamic  test  is  found  to  require  -\-  1  D.  spheric  lenses  to  arrest 
motion  of  the  shadow  for  all  proximate  distances  up  to  25  cm.; 
what  lenses  should  be  given  him  for  reading? 


144  State  Board  Examinations 

In  (his  case  +  .50  D.  represents  the  manifest  hypermetropia 
and  +  1  D.  the  total  hypermetropia,  showing  +  .50  D.  of  latent 
defect. 

As  to  what  lenses  should  be  given  him  for  reading,  we  would 
say  theoretically  +  1  D.,  which  would  he  the  correction  of  the 
total  hypermetropia.  But  in  practice  this  might  be  modified 
by  the  symptoms  of  which  the  patient  complains  and  the  ampli- 
tude of  accommodation  he  possesses.  Many  young  hyper- 
metropes  with  vigorous  accommodation  would  be  able  to  neutral- 
ize this  amount  of  hypermetropia  without  any  symptoms  of 
asthenopia. 

When  the  targets  of  an  ophthalmometer  overlap  at  angle  45 
degrees  and  separate  at  135  degrees  what  will  he  the  axis  of  the  -}- 
cylinder. 

The  meridian  in  which  the  targets  overlap  is  the  meridian 
of  greatest  refraction,  and  the  meridian  in  which  they  separate 
the  meridian  of  least  refraction.  Therefore,  45  degrees  is  the 
meridian  of  greatest  refraction,  and  13,5  degrees  the  meridian  of 
least  refraction;  the  latter  is  the  meridian  that  needs  the  assist- 
ance of  the  convex  cylinder,  and  hence  its  axis  is  placed  at  45 
degrees  to  get  its  refractive  power  at  135  degrees. 


Explain  at  length  the  reasons  for  prescribing  distance  glasses 
and  state  the  exceptions  that  may  be  made  when  ametropia  is  found. 

Distance  glasses  are  prescribed  to  improve  vision  or  to  relieve 
strain. 

In  the  first  class  of  cases  we  find  myopia,  in  which  concave 
lenses  are  necessary  to  restore  distant  vision  to  normal. 

Also  hypermetropia  existing  in  a  manifest  form,  especially 
in  middle-aged  people,  where  convex  lenses  are  needed  to  afford 
good  distant  vision. 

Also  astigmatism,  especially  myopic,  where  concave  cylinders 
are  required  for  distant  vision. 

In  the  second  class  of  cases,  there  are  hypermetropia  and 
hypermetropic  astigmatism,  where  convex  spheres  and  convex 
cylinders  may  be  required  for  constant  wear  to  relieve  strain; 


Theoretic  Optometry  145 

in  slight  degrees  occurring  in  young  persons  with  vigorous 
accommodation,  there  may  be  no  symptoms  of  asthenopia  and 
the  constant  wearing  of  glasses  may  be  deferred. 


How  should  a  preshyope  he  tested  for  muscle  imbalance  at 
14  inches;  if  this  imbalance  is  found,  what  correction,  if  any,  would 
you  give? 

The  near  test  should  be  made  with  the  reading  glasses  before 
the  eyes.  The  dot  and  line  may  be  used  in  connection  with  a 
vertical  prism  but  we  prefer  to  use  the  Maddox  rod  and  a  small 
point  of  light  14  inches  away,  such  as  can  be  obtained  from  a 
chimney  with  an  iris  diaphragm. 

Esophoria  is  but  seldom  found  and  calls  for  no  correction. 

Exophoria  is  much  more  common,  but  is  to  be  corrected 
only  in  a  small  percentage  of  cases.  This  may  be  accomplished 
by  decentering  the  convex  lenses  inwards,  or  if  more  decided 
prismatic  assistance  is  needed,  by  combining  prism,  bases  in 
with  the  spheres,  as  a  rule  correcting  not  more  than  one-half 
the  exophoria. 


In  a  compound  lens;  a  -\-  2  sphere  combined  with  a  -{-  1  cyl. 
axis  90  ,  at  what  distance  from  the  lens  will  the  image  of  a  distant 
point  have  the  form  of  a  vertical  line,  and  at  what  distance  will 
it  have  the  form  of  a  horizontal  line? 

The  power  of  this  lens  would  be  +  3  in  the  horizontal 
meridian  and  -f-  2  in  the  vertical  meridian.  The  first  focus, 
therefore,  would  be  that  of  the  horizontal  meridian  which  would 
be  located  at  13  inches,  in  the  form  of  a  vertical  line;  and  the 
second  focus  would  be  that  of  the  vertical  meridian  which  would 
be  located  at  20  inches  in  the  shape  of  a  horizontal  line, 


What  is  the  principle  of  the  construction  of  the  ophthalmometer? 

Two  bright  bodies  called  mires  are  reflected  from  the 
surface  of  the  cornea  under  examination,  after  first  being  doubled 
by  the  prisms  in  the  telescope.     The  observer  looking  through 


146  State  Board  Examinations 

the  telescope  sees  the  corneal  reflections  of  these  mires.  He  con- 
siders only  the  two  central  mires,  which  he  adjusts  so  that  they 
are  just  in  contact  in  the  meridian  of  least  refraction.  As  the 
instrument  is  turned  to  the  meridian  at  right  angles,  the  mires 
will  o\erlap,  in  this  way  showing  how  much  one  meridian  exceeds 
the  other  in  curvature.  The  guide  lines  of  the  mires  indicate 
the  location  of  the  two  principal  meridians. 

The  instrument  shows  positively  the  absence  or  presence  of 
corneal  astigmatism,  the  amount  of  same  and  the  position  of  the 
axis  of  the  correcting  cylinder. 


How  is  it  possible  to  tell  whether  a  case  is  compound,  simple 
or  mixed  astigmatism? 

In  the  use  of  the  retinoscope  if  one  meridian  was  found  to  be 
emmetropic  and  the  other  ametropic  the  case  is  simple  astigma- 
tism. If  both  meridians  are  hypermetropic  or  myopic,  varying 
in  degree,  compound  astigmatism.  If  one  meridian  is  hyper- 
metropic and  the  other  myopic,  mixed  astigmatism. 

Or  by  the  trial  case  examination,  if  a  piano  cylinder  was 
required,  the  case  is  one  of  simple  astigmatism.  If  the  sphere 
is  called  for  in  addition  to  the  cylinder,  the  case  is  compound  or 
mixed,  according  to  whether  the  signs  are  alike  or  unlike. 


//  a  prism  is  placed  in  front  of  the  eye,  base  downward,  what 
will  be  the  effect  on  the  eye  behind  that  prism? 

As  the  eye  turns  toward  the  apex  of  a  prism  in  this  case  the 
eye  will  turn  upwards. 

What  is  an  ophthalmometer?  Describe  the  principles  upon 
which  it  is  constructed  and  state  some  of  the  reasons  why  its  readings 
cannot  in  all  cases  be  relied  upon. 

The  ophthalmometer  is  an  instrument  devised  to  measure 
the  corneal  curves  and  consists  essentially  of  a  telescope  and  a 
set  of  mires.  The  latter  are  adjusted  for  the  meridian  of  least 
refraction  and  then  the  instrument  is  turned  90°  to  the  meridian 
of  greatest  refraction  and  the  difference  between  the  curvatures 
of  the  two  meridians  is  shown  at  once. 


Theoretic  Optometry  147 

As  the  scope  of  the  instrument  is  limited  to  the  measure- 
ment of  the  curvature  of  the  anterior  surface  of  the  cornea,  it  is 
evident  that  it  cannot  be  reHed  upon  in  all  cases  of  astigmatism, 
because  in  a  limited  number  of  cases  there  is  a  certain  amount 
of  lenticular  astigmatism  which  must  be  taken  into  account  in 
estimating  the  astigmatism  of  the  eye  as  a  whole.  This  lenticular 
astigmatism  may  be  static  or  dynamic,  either  of  which  changes 
the  error  as  indicated  by  the  ophthalmometer.  This  explains 
why  the  eye  will  not  always  accept  the  cylinder  representing  the 
corneal  astigmatism  as  measured  by  the  ophthalmometer. 


What  is  an  ophthalmometer? 

An  instrument  which  by  means  of  reflected  images  measures 
the  curvature  of  the  cornea  in  its  several  meridians,  and  is  used 
in  the  detection  and  measurement  of  astigmatism.  It  makes  an 
objective  test. 

What  is  a  perimeter? 

An  instrument  to  measure  the  extent  of  the  field  of  vision 
and  to  detect  the  existence  of  scotomata.  It  makes  a  subjective 
test,  but  as  it  has  reference  only  to  indirect  vision  it  is  of  no 
special  value  in  the  fitting  of  glasses. 


What  is  a  phorometer? 

Consists  of  two  prisms,  one  before  each  eye,  which  rotate 
in  conjunction,  and  it  can  be  used  not  only  to  detect  any  muscle 
imbalance,  but  to  measure  it  at  the  same  time. 


//  a  person  wore  a  3  prism,  base  out  over  one  eye  and  a  2° 
prism,  base  in,  over  the  other,  what  would  be  the  effect  of  the  same? 

The  effect  of  a  prism  base  in  is  to  neutralize  the  effect  of  a 
prism  base  out,  and  hence  in  this  case  the  prism  base  in  would 
neutralize  2  of  the  prism  base  out,  and  the  result  would  be  a 
prism  of  1    base  out. 


148  State  Board  Examinations 

If  the  far  point  with  +  4.5  sphere  is  60  cm.,  and  ivith  a  +  Z.5 
sphere  it  is  at  30  cm.,  what  is  the  refractive  condition? 

A  far  point  of  60  cm.  would  represent  a  myopia  of  1.66  D., 
and  if  this  condition  is  artificially  produced  by  a  +  4.50  D.  lens 
then  we  must  assume  the  eye  is  hypermetropic  to  the  extent  of 
the  difference  between  them,  viz.,  2.84  D. 

A  far  point  of  30  cm.  would  indicate  a  myopia  of  3).Z2)  D., 
and  if  such  myopia  is  artificially  produced  by  a  +  2.50  lens, 
then  we  infer  that  the  refraction  of  the  eye  must  be  myopic  to 
the  extent  of  the  difference  between  them,  or  .83  D. 


A  boy,  10  years,  has  a  visual  acuity  of  6/60;  with  a  -\-  3  sph. 
he  can  see  20/20,  and  the  near  point  is  at  33  cm.  What  is  probably 
the  refractive  error  in  this  case? 

In  a  case  like  this,  where  an  acuteness  of  vision  of  only  one- 
tenth  is  raised  to  normal  by  a  convex  lens,  the  refractive  error 
is  undoubtedly  hypermetropia.  But  whether  this  +  3  D. 
sphere  represents  the  full  correction  is  another  question,  on 
which  we  have  no  information.  If  normal  vision  is  reached  with 
this  lens  the  optometrist  should  not  stop  here,  but  continue 
with  stronger  lenses  as  long  as  a  vision  of  20/20  is  maintained, 
because  the  measure  of  the  error  is  the  strongest  convex  sphere 
the  patient  can  be  induced  to  accept  for  distance. 

Taking  up  the  question  of  the  optics  of  such  an  eye  from  a 
theoretic  standpoint,  if  the  +  3  D.  lenses  produced  a  near 
point  of  ?)?>  cm.  they  would  seem  to  fall  far  short  of  a  full  correc- 
tion. This  near  point  indicates  an  accommodation  of  3  D., 
whereas  the  normal  amplitude  at  this  age  is  14  D.,  showing  a 
deficiency  of  11  D.,  which  added  to  the  3  D.  would  make  14  D. 
as  the  measure  of  the  defect  in  this  eye. 

Looking  at  the  matter  from  a  practical  standpoint,  in  the 
presence  of  such  a  high  degree  of  hypermetropia,  it  would  scarcely 
be  possible  to  raise  the  vision  to  normal  by  a  -f-  3  D.  lens,  or, 
for  that  matter,  by  any  lens. 


A  patient  assisted  by  1  D.  lenses  reaches  the  punctum  proximtim 
at  33  cm.;  what  is  his  amplitude  of  accommodation? 


Theoretic  Optometry  149 

This  punctum  proximum  represents  an  amplitude  of  accom- 
modation of  3  D.  If  this  was  reached  by  the  assistance  of  1  D. 
lenses,  then  the  patient's  natural  amplitude  of  accommodation 
is  2  D. 


In  the  above  case,  what  proportion  of  the  accommodation  is 
held  in  reserve  when  +  1.5  D.  lenses  are  used  for  reading  at  33  cm.? 

In  order  for  an  emmetrope  to  read  at  d)3>  cm.,  3  D.  of  accom- 
modation is  necessary,  of  which  amount  1.50  D.  is  supplied  by 
the  convex  lenses,  and  the  other  1.50  D.  by  the  accommodation 
itself.  As  this  patient  is  said  to  have  an  amplitude  of  accom- 
modation of  2  D.,  the  amount  held  in  reserve  is  .50  D. 


A  certain  person  requires  for  distance  a  —  1.50  sph.,  and  has 
an  amplitude  of  accommodation  of  6  D.  With  what  glass  will  he 
see  most  clearly  at  a  distance  of  20  inches,  the  —  1.50  or  a  -\-  .50? 

If  a  +  .50  D.  lens  is  placed  in  front  of  this  person,  who  is 
myopic  to  the  extent  of  1.50,  his  myopia  is  increased  to  2  D., 
and  hence  this  specified  distance  of  20  inches  would  represent 
his  far  point  where  he  would  be  able  to  see  without  effort  of 
accommodation.  If,  on  the  other  hand,  the  —  1.50  D.  lenses 
were  used,  his  amplitude  of  accommodation  would  be  reduced 
to  4.50  D.,  of  which  he  would  require  2  D.  to  see  at  20  inches, 
leaving  2.50  D.  in  reserve. 

Whether  he  would  be  able  to  see  most  clearly  at  20  inches 
without  any  effort  of  accommodation,  as  in  the  one  case,  or  at 
the  expense  of  less  than  half  his  available  accommodation,  as  in 
the  other  case,  is  a  point  that  cannot  be  determined  by  any  rule. 


What  is  the  function  of  the  retina? 

To  receive  the  images  of  external  objects  as  they  are  focused 
by  the  refracting  media,  and  transfer  the  impressions  it  thus 
receives  through  the  optic  nerve  to  the  brain. 


If  patient's  vision  is  20  20  and  he  can  see  all  the  lines  on  the 
clock  dial  distinctly  and  equally,  and  can  also  read  the  very  smallest 


i 


150  State  Board  Examinations 

print  at  his  ordinary  reading  distance,  what  refractive  error  can 
he  have? 

He  might  have  a  small  amount  of  hypermetropia,  which  in 
a  young  person  is  readily  overcome  by  an  active  accommodation. 
It  is  also  likely  that  he  might  have  a  slight  hypermetropic 
astigmatism,  but  not  possible  to  have  myopia  or  myopic  astigma- 
tism. 


At  what  distance  from  the  patient  must  the  test  card  be  placed 
so  that  light  coming  from  it  will  be  practically  parallel? 

By  universal  consent  it  has  been  agreed  that  the  test  card 
shall  be  placed  at  20  feet  and  that  rays  therefrom  shall  be  assumed 
to  be  parallel  for  our  purposes  in  testing. 

Strictly  speaking,  rays  from  20  feet  have  a  divergence  of 
240  inches,  which  is  equal  to  one-sixth  of  a  diopter,  and  hence 
lenses  fitted  at  this  distance  might  be  that  much  too  strong  in 
convex  and  too  weak  in  concave. 


When  does  the  stenopaic  slit  act  best? 

We  would  say  in  myopic  astigmatism  of  marked  degree,  or 
in  hypermetropic  astigmatism  when  a  cycloplegic  has  been 
used,  as  otherwise  the  accommodation  would  make  its  results 
uncertain. 


What  is  effect  of  pupillary  distance  of  lenses  too  wide  or  too 
narrow? 

When  too  wide  the  effect  of  a  prism  base  out  in  convex  lenses, 
and  base  in  with  concave  lenses. 

When  too  narrow  the  effect  of  prism  base  in  with  convex 
lenses,  and  base  out  in  concave  lenses. 


When  should  the  pin-hole  test  be  used? 

In  all  cases  where  the  visual  acuity  is  much  impaired.  It 
would  be  of  no  value  in  cases  where  the  acuteness  of  vision  is 
normal,  or  nearly  so. 


Theoretic  Optometry  151 

With  the  vertical  lines  in  the  fan  the  blackest,  the  others  being 
dull,  blurred  or  gray,  what  is  the  axis  of  the  correcting  cylinder,  and 
what  is  the  abnormal  meridian? 

If  the  vertical  lines  are  clearest,  it  is  the  vertical  meridian 
of  the  eye  that  is  abnormal,  and  as  the  axis  of  the  cylinder  is 
placed  in  the  same  direction  as  the  indistinct  lines,  in  this  case 
the  axis  would  be  horizontal,  and  in  this  position  would  correct 
the  abnormal  vertical  meridian. 


What  is  the  purpose  of  the  test  with  the  Maddox  rod?  What 
is  tested  when  the  rod  is  vertical? 

The  purpose  of  the  Maddox  rod  is  to  form  in  the  eye  a 
retinal  image  that  is  so  dissimilar  in  size,  shape  and  appearance 
from  the  other  that  the  natural  desire  for  fusion  is  suppressed, 
thus  giving  the  eyes  over  to  the  action  of  their  muscles  and 
allowing  any  imbalance  to  become  manifest. 

When  the  rod  is  vertical  the  test  is  made  for  hyperphoria. 


State  how  you  would  measure  the  amplitude  of  accommodation 
and  the  power  of  convergence? 

By  measuring  the  closest  possible  point  of  vision  with  the 
smallest  type  and  transposing  the  same  into  diopters  will  show 
the  amplitude  of  accommodation. 

For  instance,  if  10  inches  was  the  nearest  possible  reading 
point,  the  amplitude  of  accommodation  would  be  4  D. 

The  power  of  convergence  is  measured  by  the  strongest 
prisms  bases  out  which  the  eyes  are  able  to  overcome  and  main- 
tain single  vision  of  a  point  of  light. 


In  case  of  ametropia,  by  what  means  may  a  prognosis  of  an 
improvement  in  vision  be  made  without  the  use  of  lenses? 

By  means  of  the  pin-hole  disk.  In  cases  where  the  vision 
is  greatly  impaired,  if  the  pin-hole  produces  a  decided  improve- 
ment in  vision,  we  can  assume  that  the  impairment  of  vision  is 
due  to  ametropia  and  that  an  equal  or  even  greater  improvement 


152  State  Board  Examinations 

can  be  expected  from  lenses.  Whereas  if  the  pin-hole  fails  to 
improve  vision  the  impairment  is  probably  due  to  disease  and 
glasses  would  be  useless. 

What  is  the  rule  for  correcting  hypermetropia  and  myopia 
(a)  when  the  patient  is  fifty  years  of  age  ;  (b)  when  the  patient  is 
eighteen  years  of  age?  What  is  the  rule  in  each  case  if  heterophoria 
also  is  found? 

(a)  When  patient  is  fifty  years  of  age  there  is  little  danger 
to  fear  from  the  accommodation,  and  hence  the  manifest  error 
as  found  could  be  safely  corrected,  inclining  to  the  stronger 
convex  lenses  in  hypermetropia  and  the  weaker  concave  lenses  in 
myopia. 

(b)  At  eighteen  years  of  age  in  the  presence  of  an  active 
accommodation  and  probably  more  or  less  spasm,  we  cannot 
always  give  the  convex  lenses  as  strong  in  hypermetropia  as 
we  might  like  on  account  of  the  objections  of  the  patient,  and 
yet  even  at  this  age  our  effort  always  is  to  give  convex  lenses 
as  strong  and  concave  lenses  as  weak  as  possible. 

Esophoria  in  connection  with  hypermetropia  would  indicate 
a  stronger  convex  lens,  while  exophoria  would  call  for  a  weaker 
one. 

Esophoria  in  connection  with  myopia  would  indicate  a 
weaker  concave  lens,  and  exophoria  a  stronger  one. 


Describe  two  methods  of  measuring  (a)  adduction,  (b)  abduc- 
tion, (c)  sursumduction.    State  the  theoretic  value  of  these  tests. 

By  prisms  from  the  trial  case  where  they  must  be  removed 
and  replaced  by  stronger  ones,  and  by  the  rotary  prism  where 
the  strength  can  be  gradually  increased  without  removal  from 
before  the  eye. 

(a)  Adduction  is  measured  by  the  strongest  prisms  bases 
out  which  the  eyes  are  able  to  overcome. 

(b)  Abduction  by  the  strongest  prisms  bases  in. 

(c)  Sursumduction  by  the  strongest  prisms  bases  up  or 
down. 

Theoretically  these  tests  are  supposed  to  show  the  full 
power  of  the  different  muscles. 


Theoretic  Optometry  153 

With  vision  of  20/20  what  conditions  of  refraction  may  exist.^ 

Emmetropia  or  slight  hypermetropia  or  slight  hypermetropic 
astigmatism. 

With  vision  of  20_  20  what  kinds  of  ametropia  are  eliminated? 
Myopia  and  high  degrees  of  hypermetropia  and  astigmatism. 


If  vision  at  20  feet  is  improved  by  a  —  .50  D.  Jens  what  refrac- 
tive conditions  may  exist? 

There  may  be  a  slight  degree  of  actual  myopia  or  the  refrac- 
tion may  be  emmetropic  or  hypermetropic,  in  which  a  spasm 
of  accommodation  will  cause  a  concave  lens  to  be  accepted. 


A  hyperope  with  exophoria  aged  twenty  has  20/20  vision  with 
-\-  1  D.    Is  this  the  proper  correction? 

We  are  not  told  whether  this  +  1  D.  is  the  strongest  convex 
lens  that  would  be  accepted,  but  even  if  it  is,  in  the  presence  of 
exophoria,  it  probably  does  not  represent  the  full  amount  of  the 
hypermetropia,  because  the  convergence  is  under  strain  to  over- 
come the  tendency  to  divergence.  In  order  to  measure  the 
full  refractive  error  there  must  be  relaxation  of  both  convergence 
and  accommodation,  and  this  can  be  accomplished  by  combining 
prisms  bases  in  with  the  convex  lenses,  when  it  will  probably 
be  found  that  a  stronger  than  -f  1  D.  will  be  accepted. 


With  a  prism  base  down  before  the  left  eye  the  upper  image 
is  to  the  left  of  ihe  lower  image.  What  name  is  given  to  the  con- 
dition? Why  does  the  eye  deviate?  Where  should  the  base  of  the 
correcting  prism  be  placed? 

The  condition  is  esophoria  and  diplopia  homonymous.  The 
eye  deviates  inward  either  from  excess  of  convergence  or  weak- 
ness of  divergence.    The  correcting  prism  is  placed  base  out. 


What  is  the  amplitude  of  accommodation  of  a  hypermetrope 
of  2  D.  whose  near  point  is  at  10  inches? 


1 54  State  Board  Examinations 

The  emmetropic  eye  in  order  to  see  at  10  inches  will  use  4  D. 
of  accommodation,  but  here  there  is  an  additional  2  D.  required 
to  overcome  the  hypermetropia,  hence  in  this  particular  case 
the  amplitude  of  accommodation  is  6  D. 


If  a  hypermetrope  of  2  D.  has  his  near  point  of  16  inches, 
what  is  the  amount  of  the  presbyopia  and  what  is  the  correction  for 
7iear  use? 

The  near  point  of  16  inches  shows  an  amplitude  of  accom- 
modation of  2.50  D.  For  comfortable  reading  the  person  should 
possess  5  D.  of  accommodation;  hence  there  is  a  deficiency  of 
2.50  D.  We  are  told  there  is  a  hypermetropia  of  2  D.,  and  then 
the  other  .50  D.  must  be  due  to  presbyopia  of  this  amount. 

The  correction  for  near  use  would  be  +  2.50  D.,  covering 
both  the  hypermetropia  and  the  presbyopia. 


We  are  told  to  subtract  the  far  point  from  the  near  point  for 
the  amplitude  of  accommodation  in  myopia,  and  to  add  them 
together  in  hypermetropia.     What  is  the  explanation  of  this  rule? 

In  myopia  the  amplitude  of  accommodation  seems  to  be 
greater  on  account  of  the  excess  of  refractive  power  of  the 
myopic  eye;  hence  in  order  to  find  the  actual  amplitude  of 
accommodation  we  must  subtract  the  amount  of  myopia. 

In  hypermetropia  the  amplitude  of  accommodation  seems 
to  be  diminished  on  account  of  the  deficiency  of  refractive  power 
of  the  hypermetropic  eye ;  hence  in  order  to  find  the  real  amplitude 
of  accommodation  we  must  add  the  amount  that  is  used  to  over- 
come the  hypermetropia. 

Which  tint  of  glass  is  best  for  eyes  that  are  bothered  by  sunlight? 

There  is  a  difTerence  of  opinion  on  this  point.  In  the  majority 
of  cases  smoked  glasses  will  afford  the  most  relief,  and  they  have 
the  advantage  of  not  producing  any  false  color  effects.  In  a 
certain  class  of  cases  blue  glasses  are  to  be  preferred,  because 
they  absorb  the  irritating  and  stimulating  red  rays.  Of  late 
vears   amber   glasses   have   been    recommended,    because   they 


Theoretic  Optometry  155 

suppress  the  chemical  rays  and,  while  softening  dazzling  reflec- 
tions, do  not  diminish  the  amount  of  light  admitted  to  the  eye. 
The  very  latest,  and  perhaps  the  best  tinted  lenses  are  Crookes. 


Explain  why  in  cases  of  ametropia  the  pin-hole  disk  always 
improves  vision. 

If  a  lighted  candle  be  placed  in  front  of  a  thin  metallic  plate 
having  a  small  aperture  or  pin-hole,  an  image  of  the  flame  will 
be  formed  upon  a  screen  of  white  paper  or  cardboard  that  is 
placed  back  of  it.  Most  of  the  rays  proceeding  from  the  candle 
will  be  intercepted  by  the  plate,  but  one  ray  from  each  point  of 
the  candle  will  pass  through  the  pin-hole,  and  as  they  pass  they 
cross  and  form  an  inverted  image.  The  ray  from  the  tip  of  the 
flame  forms  the  tip  of  the  inverted  image,  and  the  ray  from 
the  bottom  of  the  candle  forms  the  top  of  the  image.  A  camera 
can  be  constructed  upon  this  principle  and  photographs  made 
without  the  use  of  a  lens. 

When  impaired  vision  is  due  to  the  imperfect  focusing  of 
an  ametropic  eye  the  pin-hole  disk,  by  cutting  off  so  many  of 
the  rays,  nullifies  the  refractive  power  of  the  eye,  and  the  retinal 
image  is  formed  by  the  pin-hole  upon  the  principles  just  described. 

The  pin-hole  in  like  manner  destro^^s  the  effect  of  any  lens, 
no  matter  how  strong,  a  fact  that  can  be  easily  demonstrated. 
Take  a  moderately  strong  convex  lens  and  hold  it  close  to  the 
eye,  when  the  letters  on  the  test  card  across  the  room  will  be 
hardly  discernible  or  entirely  blotted  out.  As  soon  as  the  pin- 
hole disk  is  imposed  the  refractive  power  of  the  lens  is  destroyed 
and  the  letters  are  as  clearly  seen  as  the  naked  vision  of  the  eye 
will  allow. 


If  you  had  a  patient  forty-five  years  of  age  wearing  for  distance 
0.  U.  —  1  D.  sph.,  with  which  his  near  point  is  11  3/7  inches,  what 
will  be  his  correction  for  near  use? 

This  near  point  represents  an  amplitude  of  accommodation 
of  3.50  D.  Inasmuch  as  this  is  accomplished  through  his  distance 
glasses  of   —    1   D.  his  natural  accommodation  without  glasses 


156  State  Board  Examinations 

would  be  4.50  D.  This  would  probably  suffice  for  comfortable 
reading  without  assistance,  but  theoretically  with  the  idea  that 
the  amplitude  of  accommodation  should  not  fall  below  5  D.  a 
+  .50  D.  lens  would  be  the  proper  correction  for  near  use. 


Why  is  it  that  we  cannot  tell  from  the  test  with  the  ophthal- 
mometer the  full  astigmatic  error  of  the  eye? 

Because  it  measures  only  the  corneal  astigmatism  and  is 
unable  to  reach  the  astigmatism  that  may  be  located  in  the 
crystalline  lens. 

In  using  the  ophthalmometer  the  mires  are  brought  into  exact 
contact  in  one  principal  meridian,  and  are  then  found  to  overlap 
in  the  other  principal  meridian;  what  cylinder  is  indicated,  convex 
or  concave,  and  on  what  axis? 

If  we  knew  the  normal  curvature  of  this  particular  cornea 
for  the  first  principal  meridian  where  the  mires  were  in  exact 
contact  then  an  overlapping  w'ould  show  a  myopia  in  the  second 
meridian.  Or  if  this  second  meridian  where  the  overlapping 
occurred  was  normal  then  the  first  meridian  is  hypermetropic. 

But  as  a  matter  of  fact  we  do  not  use  the  ophthalmometer 
to  ascertain  whether  the  cylinder  should  be  convex  or  concave, 
but  to  measure  the  difference  in  power  between  the  two  principal 
meridians  (which  is  the  amount  of  astigmatism)  and  the  location 
of  these  two  meridians. 

If  a  convex  cylinder  is  required  its  axis  will  correspond  to 
the  meridian  of  overlapping;  if  a  concave  cylinder,  to  the  meridian 
which  showed  exact  contact. 


When  in  the  fogging  test  the  lines  zuhich  are  most  blurred  are 
the  vertical  lines,  in  ivhich  meridian  of  the  eye  is  the  refractive 
error,  the  vertical  or  the  horizontal? 

Ordinarily  the  answer  would  be  in  the  horizontal  meridian, 
but  this  is  true  only  in  case  of  a  hypermetropic  astigmatism  in 
which  the  fogging  lens  caused  complete  relaxation  of  the  accom- 
modation. 


Theoretic  Optometry  157 

It  is  possible  that  the  horizontal  meridian  may  be  emme- 
tropic, and  if  the  ciliary  muscle  failed  to  relax  in  response  to  the 
fogging  lens  it  would  be  made  artificially  myopic  and  cause  the 
vertical  lines  to  appear  indistinct,  when  really  the  hypermetropic 
error  would  lie  in  the  vertical  meridian. 


In  a  static  eye  fully  corrected  with  a  —  1  sph.  combined  with 
—  50  cyl.  axis  90°,  where  will  he  the  neutral  points  of  the  two 
principal  meridians  of  the  eye? 

This  correction  would  indicate  a  myopia  of  1  D.  in  the  90th 
meridian,  and  of  1.50  D.  in  the  180th  meridian;  and  the  neutral 
points  would  be  at  40  inches  and  26  inches  respectively. 


Convergent  li-ght  entering  the  eye  comes  to  an  exact  focus; 
what  kind  of  an  eye  is  it?  What  will  he  the  focus  of  far  distant 
objects  in  such  an  eye? 

The  hypermetropic  eye  is  the  only  form  of  eye  adapted  for 
convergent  rays.  If  the  accommodation  was  at  rest  the  focus 
of  parallel  rays  emanating  from  far  distant  objects  would  be 
behind  the  retina. 

A  person  fifty  years  of  age  looking  at  an  object  20  inches  away 
with  —  4  D.  sph.  'Z^  +  5  D.  cyl.  axis  90° ,  accommodates  1  D. 
What  is  the  reading  and  distance  correction? 

In  order  to  look  at  an  object  20  inches  away  2  D.  of  accom- 
modation must  be  used,  but  as  this  person  accommodates  only 
1  D.  we  must  conclude  that  the  other  1  D.  is  supplied  by  the 
uncorrected  myopia.  Hence  the  distance  correction  would  be: 
-  5  D.  sph.  O  +  5  D.  cyl.  axis  90° 
For  near  vision  we  would  add  about  +  2.50  D.,  which  would 
make  the  reading  correction: 

-  2.50  D.  sph.  O  -f  5  D.  cyl.  axis  90° 


Name   the   several   methods   of  determining   the   nature   of  a 
refractive  error. 


158  State  Board  Examinations 

Trial  case  and  test  types,  retinoscopy,  ophthalmoscopy, 
refractometer  or  optometer,  Scheiner's  test,  chromatic  test, 
measuring  amplitude  of  accommodation  and  stenopaic  slit. 


In  looking  through  a  prism  which  way  does  the  eye  turn  and 
in  which  direction  is  the  object  seemingly  displaced? 

The  eye  turns  toward  the  apex  of  the  prism  and  the  object 
is  apparently  displaced  in  the  same  direction. 


In  a  certain  lens  the  eye  first  looks  through  a  point  1  mm. 
above  the  optical  center  of  the  lens  and  then  through  a  point  I  mm. 
to  the  side  of  the  optical  center.  The  deviation  of  a  distant  object 
is  greater  in  the  first  case  than  in  the  second.  What  kind  of  a  lens 
is  it? 

Since  there  is  greater  deviation  when  looking  upward  than 
when  looking  to  the  side  there  must  be  greater  curvature  in  the 
vertical  meridian  than  in  the  horizontal.  This  would  indicate 
a  convex  sphero-cylindrical  lens,  with  the  axis  of  the  convex 
cylinder  horizontal. 


Describe  the  optical  principles  involved  in  placing  prisms  before 
the  eyes  for  the  purpose  of  ascertaining  the  powers  of  abduction 
and  adduction? 

In  orthophoric  eyes  the  image  is  assumed  to  fall  on  each 
macula  without  muscular  effort.  When  a  prism  is  placed  before 
one  or  both  eyes,  the  rays  of  light  are  turned  out  of  their  course 
and  bent  toward  the  base  of  the  prism.  Under  such  circumstances 
the  image  would  fall  on  the  retina  away  from  the  macula  and 
produce  diplopia,  except  that  the  eye  as  far  as  it  is  able  in- 
voluntarily turns  toward  the  apex  of  the  prism  in  order  to  keep 
the  image  on  the  macula  and  prevent  diplopia. 

Therefore,  when  the  prism  is  placed  base  in,  the  eye  turns 
out  in  compensation,  and  the  strongest  prism  base  in  which  the 
external  recti  muscles  are  able  to  overcome  and  maintain  bin- 
ocular vision  will  represent  the  power  of  abduction. 


Theoretic  Optometry  159 

Contrariwise,  when  the  prism  is  placed  base  out,  the  eye 
involuntarily  turns  in  as  far  as  it  is  able,  and  the  strongest  prism 
base  out  which  the  internal  recti  muscles  are  able  to  overcome 
and  maintain  binocular  vision  will  represent  the  power  of  adduc- 
tion. 


A  hypermetrope  of  2  D.  has  an  amplitude  of  accommodation 
of  4  D.  Make  the  calculation  for  lenses  to  be  used  in  reading  at 
33  cm.  so  that  one-fourth  of  the  accommodation  may  he  held  in 
reserve. 

If  it  is  desired  to  hold  in  reserve  one-fourth  of  this  4  D.  of 
amplitude  of  accommodation,  there  will  be  only  3  D.  of  accom- 
modation available  for  use,  of  which  2  D.  will  be  taken  to  over- 
come the  hypermetropia,  leaving  1  D.  for  use  in  reading.  But 
as  3  D.  is  required  for  use  at  ?>?)  cm.,  the  accommodation  must 
be  suplemented  by  a  -f  2  D.  lens. 


What  is  the  practical  value  of  the  pin-hole  disk  and  of  the 
stenopaic  disk? 

The  value  of  the  pin-hole  disk  is  to  determine  in  any  case  of 
greatly  impaired  vision  whether  it  is  due  to  an  error  of  refraction 
that  can  be  corrected  by  lenses  or  to  a  diseased  condition  that 
is  beyond  optical  assistance. 

Of  the  stenopaic  disk  to  locate  the  two  chief  meridians  of 
the  eye,  that  of  best  and  of  poorest  vision,  and  by  means  of  lenses 
placed  before  it  to  measure  the  refraction  of  those  two  meridians. 


A  patient  looks  at  a  light  20  feet  away  and  a  prism  strong  enough 
to  produce  double  vision  is  placed  base  up  before  the  right  eye;  state 
the  defect  and  its  amount  when  the  loiver  light  is  located  to  the  left  and 
a  prism  of  4°  before  one  eye  is  required  to  pluce  both  lights  in  a  vertical 
line,  and  what  will  be  the  position  of  the  4°  prism? 

If  prism  is  base  up  before  right  eye,  the  lower  image  would 
belong  to  this  eye,  and  if  located  to  the  left  would  indicate  exo- 
phoria,  to  the  extent  of  the  correcting  prism  which  is  placed  base  in. 


160  State  Board  Examinations 

On  ivhich  side  of  the  median  line  will  the  streak  of  light  pro- 
duced by  the  Maddox  rod  before  the  right  eye  appear  in  esophoria. 

Right  side. 


What  is  meant  by  the  term  refraction?  And  what  is  meant  by 
the  term  refraction  of  the  eye? 

Refraction  means  the  bending  of  rays  of  Hght  as  they  pass 
obHquely  from  one  medium  into  another  of  different  density. 

Refraction  of  the  eye  is  the  action  of  the  dioptric  media  of 
the  eye  on  the  Hght  that  enters  it  in  bringing  it  to  a  focus  either 
on  or  off  the  retina. 

It  signifies  the  optical  condition  of  the  eye,  whether  emme- 
tropic, hypermetropic  or  myopic. 


The  refraction  of  the  vertical  meridian  is  1.50  D.  hypermetropic 
and  of  the  horizontal  meridian  .25  D.  myopic.  What  is  the  prescrip- 
tion required? 

+  1.50  D.  cyl.  axis  180°  o  -  .25  D.  cyl.  axis  90°, 
or, 

+  1.50  D.  sph.  O  -  1.75  D.  cyl.  axis  90°. 


What  is  the  refractive  condition  of  an  eye  which  requires  a 
+  1.25  cyl.  axis  60°  for  reading  and  a  —  1.25  cyl.  axis  150°  for 
distance? 

Simple  myopic  astigmatism  of  1.25,  in  connection  with 
presbyopia  of  like  amount. 


The  prescription  for  a  certain  eye  is  —  .50  O  —  -25  cyl.  axis 
75°;  what  will  be  the  dioptric  power  of  the  eye  in  its  tzt'o  principal 
meridians,  assuming  that  58  D.  represents  emmetropia? 

As  myopia  acts  in  the  way  of  increasing  the  refractive  power 
of  the  eye,  there  would  be  58.50  D.  in  the  75th  meridian  and  58.75 
D.  in  the  165th  meridian. 


Theoretic  Optometry 


161 


Give  some  description  of  the  Risley  Prism  and  how  it  is  used? 

This  consists  of  two  15°  prisms  mounted  in  two  cells,  placed 
in  apposition  and  controlled  by  a  milled  head  screw.  When  so 
placed  that  the  apex  of  one  prism  lies  against  the  base  of  the 
other,  their  prismatic  power  is  neutralized,  and  their  only  effect 
is  that  of  a  thick  piece  of  glass.  As  the  milled  head  is  turned  and 
the  prisms  are  rotated  away  from  the  position  of  neutralization, 
the  effect  of  a  single  increasing  prism  is  produced,  which  reaches 
its  greatest  power  (30°)  when  the  two  bases  coincide. 

When  the  line  on  the  prism  points  to  zero  on  the  scale  in  the 
vertical  position,  a  horizontal  prismatic  power  can  be  developed 
by  rotation.  When  the  line  points  to  zero  in  the  horizontal  posi- 
tion, vertical  prismatic  power  can  be  developed  by  rotation. 

In  any  of  these  cases  the  amount  of  power  base  in,  out,  up  or 
down,  can  be  read  off  the  scale. 

The  Risley  prism  can  be  used  to  measure  the  duction  power  of 
the  various  muscles. 


The  180th  meridian  of  one  eye  is  5  D.  hypermetropic ,  and  the 
90th  meridian  6  D.  hypermetropic.  If  torics  are  prescribed,  the 
convex  curve  of  the  same  being  -\-  8  D.  sphere,  what  will  be  the  dioptric 
power  of  the  concave  surface  in  the  tivo  principal  meridians? 

This  can,  perhaps,  be  best  worked  out  and  understood  by 
diagrams. 

The  first  diagram  shows  the  desired  power  in  each  meridian. 

+  6  D. 


+  8  D. 
-  2  D. 

+  6  D. 

+  8  D. 
-  3  D. 

+  5  D. 

+  5  D. 


The  second  diagram  shows  in  order  to  maintain  these  powers 
unaltered,  how  much  concavity  must  be  added  in  each  meridian, 
viz.:  —  2  D.  in  the  vertical  meridian  and  —  3  D.  in  the  horizontal 
meridian. 


162  State  Board  Examinations 

If  a  certain  eye  has  a  poicer  in  the  90th  meridian  of  54  D.  and 
in  the  180th  meridian  53  D.,  what  sphero  cylinder  must  be  prescribed 
to  give  emmetropia  for  distance,  if,  with  the  accommodation  at  rest, 
a  perfect  retitial  image  required  the  eye  to  have  a  dioptric  power  of 
53.50  D? 

If  a  dioptric  power  of  53.5  D.  is  assumed  to  represent  emme- 
tropia, then  the  vertical  meridian  which  has  a  power  of  54  D. 
shows  an  excess  of  dioptric  power  of  .50  D.,  which  means  a  myopia 
of  Hke  amount;  and  the  horizontal  meridian  which  has  a  power 
of  .53  D.  shows  a  deficiency  of  dioptric  power  of  .50  D.,  which 
means  a  hypermetropia  of  like  amount. 

To  correct  this  condition  we  must  place  a  —  .50  D.  in  vertical 
meridian  to  reduce  it  to  53.50  D.,  and  a  +  -50  D.  in  horizontal 
meridian  to  raise  it  to  53.50  D.,  as  follows:  —  .50  D.  cyl.  axis  180° 
O  +  .50  D.  cyl.  axis  90°,  which  is  transposed  to  —  .50  D  sphere 
O  +  1  D.  cyl.  axis  90°. 


When  the  vertical  lines  on  a  clock  dial  are  clear,  and  the  hori- 
zontal are  not,  which  meridian  will  require  a  concave  cylinder  to 
correct  it? 

The  rule  is  to  pl^e  the  axis  of  the  correcting  cylinder  in  the 
same  direction  as  the  indistinct  lines,  which  in  this  case  would  be 
horizontal. 

In  seeking  the  explanation  of  this,  it  must  be  remembered 
that  the  horizontal  lines  are  seen  by  the  vertical  meridian  of  the 
eye  and  as  they  are  indistinct  in  this  case  it  must  be  because  the 
vertical  meridian  is  ametropic;  hence  we  place  the  axis  of  the 
cylinder  at  180°  in  order  to  bring  the  refractive  power  of  the  lens 
over  the  vertical  meridian,  which  is  the  one  calling  for  correction. 


How  is  it  possible  to  knoiv  with  certainty  that  an  eye  when  being' 
tested  has  been  brought  out  of  the  fog  or  not? 

It  is  safe  to  assume  the  eye  is  out  of  the  fog  when  the  acute- 
ness  of  vision  has  been  raised  to  20  20.  However,  it  may  then  be 
too  much  out  of  the  fog,  which  is  something  we  want  to  avoid, 
and,  therefore,  we  will  try  an  extra  +  .25  or  +  .50  and  see  if  it 


Theoretic  Optomelry  163 

blurs  and  how  much.    Or  better  still,  we  repeat  the  whole  proce- 
dure, taking  care  to  stop  as  soon  as  fairly  normal  vision  is  attained. 


Which  blurs  the  most,  objects  as  seen  by  a  hypermetrope,  or  as 
seen  by  a  myope,  and  why? 

This  depends  on  the  degree  of  ametropia  and  whether  refer- 
ence is  made  to  distant  or  near  objects.  With  equal  degrees  of 
defect,  vision  for  distant  objects  would  be  more  blurred  in  myopia, 
because  the  hypermetrope  is  able  by  means  of  his  accommodation 
to  neutralize  his  deficiency  of  refractive  power  and  make  vision 
normal. 

Whereas  in  myopia  the  use  of  the  accommodation  (which  is 
the  only  function  we  possess  to  influence  the  distinctness  of  the 
retinal  image)  would  make  the  blurred  vision  still  more  indistinct. 

But  there  are  some  cases  of  high  hypermetropia  in  which 
vision  is  very  much  impaired,  and  the  accommodation  is  unable 
to  raise  it  to  normal,  probably  on  account  of  the  undeveloped 
condition  of  the  eyeball. 

What  is  meant  by  the  term  "meridian  of  greatest  refraction,'' 

and  hotv  is  it  known? 

■f 

In  regular  astigmatism  there  are  two  principal  meridians,  one 
of  greatest  and  one  of  least  curvature  at  right  angles  to  each  other. 
In  myopic  astigmatism  the  meridian  of  greatest  refraction  is  that 
meridian  which  shows  the  most  myopia,  and  in  hypermetropic 
astigmatism  the  one  showing  least  hypermetropia.  In  the  first 
case  it  is  the  meridian  right  angles  to  the  axis  of  the  concave 
cylinder;  and  in  the  second  the  meridian  that  corresponds  to  the 
axis  of  the  convex  cylinder. 

It  may  be  detected  by  the  fogging  method  used  in  two  ways: 

Fog  first  a  set  of  vertical  lines  and  then  a  set  of  horizontal 
lines,  and  the  meridian  of  greatest  refractive  power  would  cor- 
respond to  the  direction  of  the  lines  that  can  be  seen  with  the 
strongest  convex  sphere. 

Or  fogging  the  whole  astigmatic  dial,  it  is  in  the  same  direc- 
tion as  the  lines  that  first  come  out  of  the  fog. 

Or  it  can  be  found  by  the  retinoscope  which  measures  the 
refraction  of  each  meridian  in  turn. 


164  State  Board  Examinations 

When  are  parallel  lines  as  shoicn  on  astigmatic  charts  reliable, 
and  when  not^'' 

These  parallel  lines  radiate  in  all  directions,  and  they  are  to 
be  relied  upon  as  a  test  for  astigmatism  only  when  the  accommo- 
dation is  at  rest  (as  in  fogging),  as  otherwise  the  patient  would 
instinctively  make  an  effort  to  clear  the  lines,  and  thus  mask  the 
astigmatism  or  lead  to  an  incorrect  diagnosis. 


Which  should  be  corrected  first  in  retinoscopy,  the  spherical 
error  or  the  astigmatic  error,  and  what  is  the  reason? 

The  writer  thinks  it  is  best  to  correct  first  the  meridian  of 
least  refraction,  and  then  the  meridian  of  greatest  refraction.  The 
first  would  represent  the  spherical  error  and  the  difterence  between 
the  two  the  astigmatic  error. 


When  should  a  person  with  high  astigmatism  get  normal  vision 
with  his  correction,  and  when  would  this  not  be  true? 

Sometimes  it  is  impossible  in  high  astigmatism  to  afi^ord  nor- 
mal acuteness  of  vision,  and  this  is  especially  true  if  the  error  is 
not  corrected  until  later  in  life.  If,  however,  cylindrical  lenses 
had  been  worn  from  an  early  age,  and  they  needed  changing  as 
they  usually  do  from  time  to  time,  we  would  expect  the  new 
lenses  to  give  fair  vision  if  there  is  not  too  much  difterence  in  the 
strength  of  the  lenses  or  the  position  of  the  axis  from  the  previous 
ones. 

Where  glasses  had  not  been  previously  worn  and  the  sensi- 
bility of  the  retina  was  blunted  by  the  imperfect  images  focused 
upon  it,  vision  with  the  cylinders  will  be  more  or  less  unsatisfac- 
tory, although  we  would  expect  it  to  improve  with  the  constant 
wearing  of  the  glasses. 


How  is  the  test  for  adduction  usually  made? 

By  prisms  bases  out  gradually  increased  in  strength.  The 
strongest  prisms  with  which  single  vision  of  a  light  can  be  main- 
tained represent  the  power  of  adduction.  This  is  a  variable  quan- 


Theoretic  Optometry  165 

tity  and  ranges  from  15°  to  40°  or  higher,  and  can  be  greatly 
increased  by  exercise. 

When  two  plus  lenses  of  different  power  give  eqiiaUy  good 
vision,  why  is  the  stronger  one  selected? 

We  presume  that  this  has  reference  to  the  tests  for  distant 
vision  in  hypermetropia,  in  which  the  rule  is  to  select  the  strong- 
est convex  lens  the  patient  can  be  made  to  accept,  for  the  reason 
that  the  stronger  the  lens,  the  more  of  the  hypermetropia  it  cor- 
rects and  the  less  effort  on  the  part  of  the  accommodation  is 
required. 

//  a  patient  has  astigmatism  which  requires  a  -\-  2  D.  cylinder 
axis  horizontal  to  correct,  and  you  place  a  -\-  2  D.  sphere  before  the 
eye,  what  artificial  condition  is  produced? 

The  +  2  D.  sphere  corrects  the  hypermetropic  meridian,  but 
at  the  same  time  it  blurs  the  emmetropic  meridian  and  makes  it 
myopic  to  the  extent  of  2  D.  Therefore,  the  artificial  condition 
produced  is  simply  myopic  astigmatism,  at  right  angles  to  the 
original  hypermetropic  astigmatism. 


What  is  the  principal  purpose  of  each  of  the  folloicnng  instru- 
ments:  ophthalmoscope ,  retinoscope  and  ophthalmometer? 

The  ophthalmoscope,  to  examine  the  interior  of  the  eyeball 
as  to  the  presence  or  absence  of  disease,  and  if  disease  is  present 
to  determine  its  location  and  nature. 

The  retinoscope,  to  measure  the  refractive  condition  of  the 
eye. 

The  ophthalmometer,  to  detect  and  measure  corneal  astig- 
matism as  to  its  amount  and  the  location  of  the  two  principal 
meridians. 

Under  what  conditions  may  a  person  have  an  amplitude  of 
accommodation  of  3  D.  and  still  have  no  range  of  vision? 

When  hypermetropia  is  present  to  an  equal  or  greater 
amount. 


166  State  Board  Examinations 

If  a  patient  has  myopic  astigmatism,  imder  what  conditions 
u'oiild  a  plus  cylinder  be  proper  to  prescribe? 

For  reading  after  presbyopia  has  set  in.  For  instance,  if  a 
patient  wearing  —ID.  cyl-  axis  180°  reaches  45  years  of  age, 
when  the  addition  of  +  1  D.  is  needed  for  reading,  the  prescrip- 
tion would  be  +  1  D.  cyl.  axis  90°. 


//  light  coming  from  a  distance  of  20  inches  is  exactly  focused 
on  the  retina  with  a  -\-  3  D.  lens  and  with  the  accommodation  at 
rest,  ivhat  is  the  kind  and  amount  of  refractive  error?  Hoiv  do  you 
calcidate  the  restdt? 

Light  coming  from  a  distance  of  20  inches  has  such  a  degree 
of  divergence  that  requires  +  2  D.  lens  to  focus  it  upon  the  retina 
of  an  eye  with  the  accommodation  at  rest. 

If,  however,  as  in  this  case,  a  +  3  D.  lens  is  required,  then 
we  must  assume  that  the  extra  +  1  D.  represents  a  deficiency  in 
the  refractive  power  of  the  eye  of  that  amount  or  in  other  words 
a  hyper metropia  of  1  D. 

Hoiv  ivoidd  yon  test  the  strength  of  any  particjdar  ocular  muscle 
with  prisms? 

By  placing  apex  of  prism  over  such  muscle  and  finding  strong- 
est prism  with  which  binocular  vision  can  be  maintained. 


What  is  the  main  purpose  of  the  ophthalmometer? 

To  determine  the  curvatures  of  the  cornea,  the  location  of 
the  two  principal  meridians  and  the  refractive  power  of  each 
meridian. 


If  a  person  50  years  of  age  came  to  you  ivearing  a  pair  of  bifocals 
of  ivhich  the  power  was  3.50  D.,  what  error  in  the  distance  correction 
would  you  suspect? 

We  assume  that  +  3.50  D.  is  meant  to  indicate  the  power  of 
the  segments,  in  which  case  we  would  say  the  distance  was  under- 


Theoretic  Optometry  167 

corrected;  for  the  reason  that  at  this  age  the  segment  scarcely 
exceeds  2  D.  or  in  other  words  the  presbyopia  is  seldom  greater 
than  this.  Hence  the  3.50  D.  segments  are  correcting  some  of 
the  hypermetropia,  which  should  have  been  provided  for  in  the 
distance  lenses. 


A  child  showing  with  the  objective  tests  5  D.  of  hypermetropia 
sees  clearly  with  +  1.50  D.  lenses,  while  anything  stronger  blurs 
the  letters.  What  would  you  give  and  how  would  you  handle  the 
case? 

This  would  depend  somewhat  on  the  age  of  the  child  and 
the  symptoms  of  which  he  complains.  As  a  rule  children  will 
bear  fogging  better  than  adults,  therefore,  if  the  child  were 
quite  young  and  the  symptoms  urgent,  we  would  give  +  2.50  D. 
for  constant  wear. 

If  the  child  was  older  and  likely  to  object  to  the  fogging, 
we  would  attempt  to  correct  only  the  manifest  hypermetropia 
at  first  with  -f  1.50  D.  lenses,  in  the  thought  that  after  a  while 
some  of  the  latent  defect  would  become  manifest  when  the 
strength  of  the  glasses  could  be  increased.  After  these  second 
glasses  had  been  worn  for  a  time,  perhaps  another  increase  could 
be  borne,  if  the  symptoms  were  such  as  to  call  for  more  relief. 


What  method  would  you  employ  to  find  the  amount  of  latent 
hypermetropia?  Can  the  latent  be  estimated  from  the  amoiint  of 
manifest? 

I  would  employ  the  fogging  method  to  estimate  as  far  as 
possible  the  total  hypermetropia,  and  the  difference  between 
that  and  the  manifest  hypermetropia  would  represent  the  latent. 

Or  if  it  was  not  possible  to  discover  any  latent  error  in  this 
way,  I  would  correct  the  manifest  with  the  thought  that  under 
such  correction  some  of  the  latent  would  gradually  become 
manifest. 

The  amount  of  latent  bears  no  constant  relation  to  the 
amount  of  manifest  error;  in  youth  it  is  nearly  all  latent  and  in 
old  age  it  is  nearly  all  manifest. 


168  State  Board  Examinations 

If  the  internal  recti  muscles  were  weak,  how  ivoitid  the  prism 
exercise  be  i^ivoi  to  make  them  stroni^er? 

As  the  apex  of  the  prism  is  always  to  be  placed  over  the 
muscle  to  be  exercised,  the  prisms  in  this  case  are  to  be  placed 
bases  out. 

The  first  point  is  to  ascertain  the  power  of  the  internal  recti 
and  thus  determine  how  far  they  fall  below  the  normal  standard, 
which  is  accomplished  by  means  of  prisms  bases  out,  the  strongest 
with  which  single  vision  of  a  light  can  be  maintained.  This  may 
fall  to  10°  or  less  as  compared  with  the  normal  power  of  conver- 
gence, which  is  from  20°  to  30°. 

Having  found  this  strongest  prism,  it  is  divided  between  the 
two  eyes  and  alternately  raised  and  lowered.  Each  time  the 
prisms  are  lowered  the  light  is  probably  seen  double  momentarily, 
but  is  quickly  brought  into  one  by  the  action  of  the  internal 
recti.  The  raising  of  the  prisms  allows  these  muscles  to  relax 
a  little  and  get  a  slight  rest,  and  their  lowering  calls  the  muscles 
into  action  again. 

This  alternate  relaxation  and  contraction  stimulates  the 
innervation  and  circulation  of  the  muscles,  and  it  is  soon  found 
that  stronger  prisms  can  be  overcome,  and  hence  they  are 
gradually  strengthened  as  the  increasing  power  of  convergence 
will  allow. 


A  myope  is  found  to  be  ivearing  his  spectacles  each  —  10  D. 
sphere  tilted  so  that  the  right  glass  is  5  mm.  above  the  center  of  his 
pupil  and  the  left  glass  is  5  mm.  below.  What  will  be  the  effect  on 
his  vision  and  how  many  degrees  would  it  displace  the  image  at 
3  meters? 

According  to  the  rule  of  decentration  that  there  would  be  1° 
prismatic  effect  for  each  diopter  of  refractive  power  when 
decentered  10  mm.,  there  would  be  5°  prism  power  added  to  the 
concave  lens  in  each  eye.  In  the  right  eye  the  prismatic  effect 
would  be  base  down,  which  causes  a  displacement  upward  of 
object  looked  at,  and  in  left  eye  base  up  causing  displacement 
downward. 

As  the  vertical  muscles  are  comparatively  weak  and  easily 
thrown  out  of  balance,  such  tilting  of  the  lenses  would  almost 


Theoretic  Optometry  169 

certainly  cause  diplopia,  unless  there  was  a  condition  of  right 
hyperphoria,  which  would  be  corrected  by  such  position  of  the 
lenses. 

Inasmuch  as  the  above  figures  apply  for  each  meter  of 
distance,  the  displacement  at  3  meters  would  Ije  three  times  as 
great. 

A  person  requires  for  the  right  eye  alone  —  6  D.  sphere  for 
distance  and  —  3D.  sphere  for  reading,  but  luants  only  one  pair 
of  spectacles.  State  the  various  ivays  in  which  this  can  he  managed, 
and  which  method  you  prefer. 

As  the  question  states  the  glasses  are  required  for  the  right 
eye  alone,  we  must  assume  that  the  left  eye  is  useless  as  an  organ 
of  vision,  and  the  effect  of  the  proper  glass  before  the  right 
eye  can  be  obtained  in  one  of  several  ways. 

1.  By  using  a  reversible  eyeglass  frame  with  regular  guards, 
or  reversible  spectacles  with  a  C  or  X  bridge,  and  placing  a  —  6 
D.  lens  in  one  of  the  eyepieces  of  the  frame  and  a  —  3  D.  lens 
in  the  other  eye  wire,  which  will  allow  the  lens  desired  to  be 
placed  before  the  right  eye  at  will. 

2.  By  a  frame  fitted  with  —  6  D.  lenses  and  a  hook  front 
fitted  with  +  3  D.  lenses. 

3.  By  a  frame  fitted  with  —  3D.  lenses  and  a  hook  front 
fitted  with   —  3D.  lenses. 

4.  By  giving  bifocals,  with  —  6  D.  for  distance  and  +  3 
added  for  reading. 

What  is  the  effect  of  having  strong  lenses  placed  too  far  from 
the  eye? 

As  a  strong  convex  lens  is  moved  away  from  the  eye  the 
object  seems  to  approach  and  is  magnified;  as  a  concave  lens  is 
moved  away  the  object  seems  to  recede  and  is  minified. 


In  testing  an  eye  with  the  stenopaic  slit  and  using  a  set  of 
parallel  test  lines  as  the  object  of  regard,  how  should  these  lines 
be  arranged  in  reference  to  the  direction  of  the  slit? 

Vertical  lines  are  seen  by  the  horizontal  meridian  of  the 


170  State  Board  Examinations 

eye  and  horizontal  lines  by  the  vertical  meridian ;  hence  the  lines 
should  always  be  at  right  angles  to  the  direction  of  the  slit. 

But  as  a  matter  of  fact  the  card  of  test  letters  should  be 
used  in  connection  with  the  stenopaic  slit  and  not  the  card  of 
radiating  lines. 


On  -what  principle  are  the  sizes  of  the  letters  on  the  test  chart 
determined^ 

Inasmuch  as  a  visual  angle  of  one  minute  is  the  smallest 
that  can  be  perceived,  the  test  letters  are  made  of  such  size 
that  the  width  of  each  line  of  the  letter  at  its  proper  distance 
from  the  eye  will  form  an  angle  of  one  minute,  while  the  whole 
letter  will  form  an  angle  of  five  minutes. 


//  a  cylinder  is  placed  before  the  emmetropic  eye  and  two  sets 
of  lines  are  looked  at,  one  agreeing  with  the  axis  of  the  cylinder  and 
the  other  at  right  angles  to  this,  will  one  set  of  lines  be  seen  best? 

Assuming  the  eye  to  be  in  a  static  condition,  the  lines  agreeing 
with  the  axis  of  the  cylinder  will  be  more  or  less  blurred  according 
to  the  nature  and  strength  of  the  cylinder,  while  the  lines  at 
right  angles  to  this  will  be  unimpaired  because  seen  through 
the  axis  of  the  cylinder,  which  is  piano,  always  bearing  in  mind 
the  fact  that  vertical  lines  are  seen  by  horizontal  meridian  of 
eye,  and  horizontal  lines  by  vertical  meridian  of  eye. 


A  pinhole  disk  is  usually  claimed  as  showing  whether  a 
refractive  error  is  present  or  not.  Under  what  condition  would 
this  not  be  correct? 

If  in  a  case  of  impaired  vision  the  pinhole  disk  raised  it  to 
normal,  we  are  justified  in  saying  a  refractive  error  is  present. 
If,  however,  there  was  opacity  of  any  refracting  medium  or 
atrophy  of  the  optic  nerve,  there  could  be  no  improvement  in 
vision  on  this  account,  and  yet  there  might  be  an  error  of  refrac- 
tion in  addition. 


Theoretic  Optometry  171 

//  a?i  eye  is  2  D.  hypermetropic  in  the  vertical  meridia^i  and 
yon  place  a  -\-  2  sphere  in  front  of  this  eye,  ivhat  is  the  condition 
thus  artificially  produced? 

This  +  2  D.  sphere  will  correct  the  vertical  hypermetropic 
meridian  and  make  it  emmetropic,  but  at  the  same  time  it  will 
make  the  emmetropic  horizontal  meridian  artificially  myopic 
to  the  extent  of  2  D. 


Which  set  of  lines  in  a  cross-dial  chart  shows  the  axis  of  the 
astigmatism? 

The  horizontal  lines  are  seen  by  the  vertical  meridian  of 
the  eye,  and  the  vertical  lines  by  the  horizontal  meridian  of  the 
eye.  Therefore,  if  the  horizontal  lines  are  indistinct,  the  vertical 
meridian  of  the  eye  is  assumed  to  be  defective;  and  if  the  \ertical 
lines  are  indistinct,  we  assume  that  the  horizontal  meridian  of 
the  eye  is  defective. 

It  must  be  further  remembered  that  the  meridian  of  the 
axis  of  a  cylinder  is  plane  and  that  the  refractive  power  lies  in 
the  meridian  at  right  angles  thereto.  Hence  we  place  the  axis 
at  right  angles  to  the  defective  meridian;  and  the  indistinct  lines 
are  also  at  right  angles  to  the  defective  meridian,  and  therefore 
the  axis  must  be  in  the  same  meridian  as  the  indistinct  lines. 

But  suppose  the  defective  meridian  was  hypermetropic  and 
the  accommodation  came  into  action,  as  is  likely  to  be  the  case; 
then  the  naturally  ametropic  meridian  is  made  artificially  emme- 
tropic, and  the  naturally  emmetropic  meridian  is  made  artificially 
ametropic,  and  under  these  circumstances  the  rule  mentioned 
above  will  not  apply  at  all  as  the  axes  are  reversed. 

For  instance,  in  a  case  of  simple  hypermetropic  astigmatism 
with  the  rule,  the  proper  correcting  lens  is  a  +  cyl.  axis  90°; 
but  if  the  accommodation  is  allowed  to  come  into  play,  the  lens 
accepted  would  be  a  —  cyl.  axis  180°. 

Therefore,  the  use  of  the  cross  lines  to  determine  the  location 
for  the  axis  of  the  cylinder  is  of  value  only  when  the  accommoda- 
tion is  kept  passive,  as  in  the  fogging  method  when  it  is  repressed 
by  a  convex  lens. 

What  is  meant  by  exercise  of  the  muscles  or  ocular  gynuiastics? 


172  State  Board  Examinations 

In  cases  of  heterophoria,  after  the  proper  lenses  have  been 
gi\-en  to  correct  the  error  of  refraction,  and  perhaps  the  patient 
referred  to  his  family  physician  to  have  his  general  health  looked 
after,  an  effort  may  he  made  to  strengthen  the  weak  muscles  by 
systematic  exercise,  to  which  the  term  "ocular  gymnastics"  has 
been  applied. 

The  most  promising  cases  are  those  of  exophoria  due  to  an 
insufficiency  of  the  internal  recti,  which  set  of  muscles  we  try 
to  strengthen  by  exercise. 

In  the  first  exercise  the  patient  is  directed  to  take  a  pencil 
and  hold  it  at  arm's  length  in  a  perpendicular  position.  It 
should  be  held  in  the  median  line  in  front  and  gradually 
approached  while  the  top  of  the  pencil  is  fixed  by  the  two  eyes. 
When  it  gets  to  within  a  few  inches  from  the  eyes,  the  pencil 
is  seen  double,  when  it  should  at  once  be  pushed  off  the  starting 
point  and  the  procedure  done  over  again.  This  exercise  can  be 
kept  up  for  five  or  ten  minutes  (if  it  does  not  nauseate  the  patient, 
as  sometimes  happens)  and  repeated  daily. 

The  second  exercise  is  by  means  of  prisms  placed  over  the 
eyes  bases  out,  commencing  with  weak  numbers  and  gradually 
increasing  their  strength  while  the  patient  looks  at  a  point  of 
light  across  the  room.  The  strongest  prisms  are  found  which 
can  be  overcome  and  with  which  singleness  of  vision  of  the  light 
can  be  maintained  for  a  moment  or  two,  and  they  will  represent 
the  present  power  of  adduction. 

Then  the  prisms  are  raised  for  a  few  seconds,  and  as  they 
are  lowered  again  diplopia  is  evident  for  an  instant,  but  soon 
disappears.  The  prisms  should  be  raised  and  lowered  every 
thirty  seconds  for  half  a  dozen  times,  when  the  prisms  may  be 
increased  2°.  If  his  increase  can  be  easily  overcome,  the  prisms 
should  be  raised  and  lowered  another  half  dozen  times. 

The  idea  to  be  kept  in  mind  is  to  gradually  increase  the 
prisms  about  2°  at  a  time.  The  optometrist  must  use  his  judg- 
ment and  not  try  to  increase  them  too  fast.  This  point  can 
usually  be  determined  by  the  readiness  with  which  the  temporary 
diplopia  caused  by  dropping  the  prisms  into  place  can  be  over- 
come. If  the  two  lights  run  together  as  quick  as  a  flash,  then 
probably  stronger  prisms  can  be  overcome  and  should  be  tried. 


Theoretic  Optometry  173 

At  the  start,  perhaps  the  eyes  cannot  overcome  more  than 
6°  or  8°,  but  as  the  muscles  strengthen  under  the  exercise  and 
their  innervation  is  stimulated,  the  prisms  can  be  increased  up 
to  40°  or  50°.  The  exercises  should  be  continued  until  this 
point  is  reached,  because  after  they  are  stopped  some  of  the 
adduction  power  thus  developed  must  be  expected  to  disappear. 


Practical  Optometry 

What  is  the  relation  betiveen  prisms  marked  in  degrees  and 
prisms  marked  in  prism  diopters,  and  what  is  the  relation  hetzueen 
the  value  as  marked  on  prisms  and  their  deflating  poiver? 

In  the  case  of  prisms  marked  in  degrees  we  say  they  are 
numbered  by  the  refracting  angle  of  the  two  surfaces  of  the  glass 
where  they  meet  at  the  edge  or  apex,  founded  on  the  fact  that 
there  are  360°  in  a  circle  and  that  l/360th  part  of  a  circle  would 
represent  a  prism  of  1°. 

In  the  case  of  prisms  numbered  in  prism  diopters  the  unit  of 
this  method  of  numbering  is  a  prism  diopter  (which  may  be 
abbreviated  P.  D.  or  A)  which  will  deviate  a  ray  of  light  just 
1  cm.  at  a  distance  of  1  meter,  or  2  cm.  for  2  meters,  3  cm.  for 
3  meters  and  so  on  in  the  same  proportion  for  all  distances,  no 
matter  what  the  index  of  refraction  of  the  glass  used  may  be. 

A  comparison  of  prisms  marked  in  degrees  with  those  num- 
bered by  prism  diopters  will  show  them  to  have  nearly  the  same 
value;  in  fact,  the  difference  is  so  slight  that  they  can  be  used 
interchangeabh'  in  practice. 

The  relation  between  the  number  marked  on  the  prism  and 
its  deviating  power  is  as  2  to  1.  That  is,  the  angle  of  deviation  is 
equal  to  about  one-half  the  angle  of  the  prism,  which  applies  to 
all  prisms  of  ten  degrees  or  less.  In  prisms  of  a  higher  power  the 
angle  of  deviation  increases. 


When  prisms  are  ordered  in  a  prescription  how  would  you  know 
that  the  prisms  have  been  ground  in  the  lens? 

The  first  point  to  be  looked  for  is  a  difference  in  thickness  in 
the  two  opposite  sides  of  the  lens,  comparing  the  inner  and  outer 
edges  together,  and  the  upper  and  lower. 

Then  we  look  to  see  if  the  lens  shows  the  deviating  effect  of 
a  prism  by  holding  it  in  front  of  the  eye  at  some  little  distance  and 
viewing  ^  straight  edge  or  line  across  the  room.     If  the  prescrip- 

174 


Practical  Optometry  175 

tion  calls  for  a  lens  of  refractive  power  combined  with  the  prism, 
we  must  be  careful  to  look  directly  through  the  optical  center  of 
the  lens,  as  otherwise  the  deviating  power  developed  by  looking 
through  any  refractive  lens  at  a  point  away  from  its  center  will 
interfere  with  our  efforts  to  detect  the  real  prism  in  the  combi- 
nation. Perhaps  the  better  way  would  be  to  first  neutralize  the 
refracting  power  of  the  lens  and  even  here  we  must  have  a  care 
to  see  that  its  optical  center  shall  exactly  coincide  with  the  optical 
center  of  the  neutralizing  lens  and  then  the  presence  of  a  prism 
becomes  evident  by  a  break  in  the  line,  no  matter  what  part  of  the 
lens  Ave  look  through. 

Does  decentering  a  sphere  make  a  sphero-prism,  or  to  make  a 
sphero-prism  must  the  sphere  be  on  one  side  and  the  prism  on  the 
other? 

The  decentration  of  a  sphere  makes  manifest  its  prismatic 
power,  which  then  has  the  value  of  a  sphero-prism,  although  it  is 
only  a  spherical  lens. 

It  would  be  impossible  to  have  a  prism  on  one  surface  of  a 
lens,  because  a  prism  depends  upon  its  two  plane  surfaces  being 
inclined  to  each  other,  hence  one  surface  of  a  lens  could  not  show 
the  effect  of  a  prism.  When  a  sphero-prism  is  ordered,  a  plane 
prism  is  taken  and  the  desired  spherical  curvature  is  ground  on 
one  of  its  surfaces,  the  other  surface  remaining  plane. 


Upon  what  optical  principle  is  the  use  of  the  Maddox  rod  based? 

The  Maddox  rod  produces  very  great  magnification  at  right 
angles  to  its  axis,  elongating  a  small  flame  into  a  long  streak  of 
light.  This  result  is  such  a  great  dissimilarity  in  the  size,  shape  and 
appearance  of  the  two  retinal  images  that  they  cannot  be  fused 
into  one,  and  as  the  eyes  abandon  the  attempt  to  effect  fusion, 
each  eye  is  left  to  the  action  of  its  muscles  and  the  eyes  assume 
the  position  of  unstrained  equilibrium.  Under  these  circumstances 
the  position  which  the  streak  assumes  with  reference  to  the  light 
will  indicate  either  orthophoria  or  heterophoria. 


Which  position  should  be  given  to  the  prism  placed  on  the 
Maddox  rod  before  the  normal  right  eye  so  as  to  deflect  the  observed 


176  State  Board  Exam  iu  at  ions 

vertical  line  of  liiilit  12  cm.  to  the  left  at  6  meters  distance?     What  is 
the  poicer  of  the  prism? 

The  displacement  of  objects  viewed  through  a  prism  is  always 
in  the  direction  of  the  apex;  therefore,  in  this  case  where  it  is 
desired  to  move  the  right  image  inwards  or  to  the  left,  the  prism 
would  have  to  be  placed  base  out  over  right  eye. 

Inasmuch  as  a  prism  diopter  causes  a  deviation  in  a  ray  of 
light  in  the  ratio  of  1  cm.  for  each  meter  of  distance,  there  will 
be  a  deviation  of  3  cm.  for  3  meters  and  6  cm.  for  6  meters.  In 
this  case  where  the  deviation  is  12  cm.  for  6  meters,  the  power  of 
the  prism  would  be  2 A. 


I7i  which  position  must  the  prism  bases  be  placed  to  ascertain 
the  poivers  of  adduction,  abduction,  supraduction  and  infraduction, 
respectively? 

Adduction,  bases  out. 
Abduction,  bases  in. 
Supraduction,  bases  down. 
Infraduction,  bases  up. 


Would  you  always  prescribe  glasses  where  ametropia  is  found 
to  exist?    If  not,  state  exceptions. 

No;  in  slight  degrees  of  defect,  where  vision  was  but  little 
if  any  impaired,  and  where  there  were  no  symptoms  complained 
of,  glasses  would  scarcely  be  justified;  especially  if  slight  hyper- 
metropia  existed  with  exophoria,  or  low  myopia  with  esophoria. 


With  the  Maddox  rod  horizontal  before  the  left  eye,  the  point 
of  light  being  at  six  meters  and  the  streak  appearing  12  cm.  to  the 
right  of  the  point,  what  is  the  kind  and  amount  of  heterophoria  and 
in  which  direction  would  you  place  the  base  of  a  prism  to  bring  the 
streak  through  the  point  of  light? 

As  the  diplopia  in  this  case  is  crossed  the  condition  is  one 
of  exophoria. 


Practical  Optomzlry  177 

The  deviation  of  one  prism  diopter  is  1  cm.  for  each  meter 
of  distance,  which  would  mean  6  cm.  for  6m.  Therefore,  a  dis- 
placement of  12  cm.  would  indicate  2  A  of  exophoria. 

The  base  of  prism  is  placed  in  to  bring  the  streak  through 
the  light. 

A  plus  4  diopter  lens  is  the  correction  called  for  in  a  case  of 
hypermetropia.  What  is  the  effect  of  wearing  this  lens  too  far  from 
the  eye,  say  an  inch,  as,  for  instance,  where  the  spectacles  are  pushed 
far  down  on  the  nose? 

The  effect  of  pushing  the  lens  forward  is  to  increase  its 
strength.  Therefore  if  +  4  D.  is  the  proper  correction  in  the  usual 
position,  it  would  be  too  strong  when  worn  far  down  the  nose. 


//  rays  of  light  from  a  distance  of  20  inches  are  focused  on 
the  retina  with  a  plus  2  D.  lens  without  accommodation,  what  is  the 
refractive  error? 

Rays  of  light  diverging  from  a  distance  of  20  inches  and 
passing  through  a  convex  lens  of  2  D.  would  emerge  parallel, 
and  if  such  rays  were  focused  on  the  retina  without  accommo- 
dation, the  eye  must  be  emmetropic. 


What  is  the  ametropic  correction  for  a  patient,  age  twenty 
years,  with  his  near  point  of  the  vertical  meridian  at  8  inches  and 
the  near  point  of  the  horizontal  meridian  at  10  inches? 

The  emmetropic  eye  at  20  years  of  age  possesses  10  D. 
amplitude  of  accommodation  in  both  meridians. 

In  this  case  a  near  point  of  8  inches  in  the  vertical  meridian 
shows  5  D.  of  accommodation  for  this  meridian,  which  is  a 
deficiency  of  5  D.  and  a  probable  hypermetropia  of  this  amount. 
In  the  horizontal  meridian  the  near  point  of  10  inches  shows  4  D. 
of  accommodation  on  a  deficiency  of  6  D.  and  a  probable  hyper- 
metropia of  this  amount.  This  would  be  compound  hyper- 
metropic astigmatism  and  the  correction  reads  as  follows: 
-f  5  D.  sph.  O  +  1  D.  cyl.  axis  90° 


178  State  Board  Examinations 

What  is  the  correct  prescription  for  distance,  for  a  patietit 
aged  thirty  years,  looking  at  13  inches  with  his  focus  on  the  retina, 
while  wearing  a  -\-  2  sphere  on  a  —3  cyl.  axis  90°,  using  2  D.  of 
accommodation  i^ 

An  emmetropic  eye  looking  at  13  inches  uses  3  D.  of  accom- 
modation. If,  however,  in  this  case  a  +  2  D.  sphere  is  worn  and 
in  addition  it  is  necessary  to  use  2  D.  of  accommodation,  then 
this  4  D.  would  indicate  that  1  D.  more  than  in  emmetropia 
is  necessary,  revealing  a  hypermetropia  of  this  amount;  therefore 
the  correct  prescription  for  distance  would  be 

+  1  D.  sph.  C  -  3  D.  cyl.  axis  90° 


A  patient  is  told  to  look  at  a  small  light  20  feet  away  and  is 
given  diplopia  with  a  prism,  base  down,  before  the  right  eye.  What 
defect  and  amount  of  error  are  present  when  the  upper  light  is 
located  to  the  right,  and  a  prism  of  3°  before  each  eye  is  required 
to  bring  both  lights  to  the  median  line^  What  is  the  position  of  the 
3°  prisms? 

If  the  prism  is  base  down  before  right  eye  then  the  right 
image  belongs  to  right  eye  and  the  condition  is  one  of  esophoria. 
The  correcting  prisms  of  3°  must  be  placed  bases  out  to  bring  the 
lights  one  under  the  other. 


A  myope  of  3  D.  sees  w'ith  his  right  eye  the  Maddox  rod  line 
9  cm.  lower  than  the  object  light.  Write  the  prescription  for  distance 
lenses,  lenses  to  be  0  eye,  so  that  the  least  cost  will  be  incurred. 

The  deviation  caused  b}'  one  prism  diopter  is  1  cm.  for  each 
meter  distance.  Presuming  this  test  was  made  at  the  usual  dis- 
tance of  6  meters,  the  deviation  would  equal  6  cm.  The  question 
says  there  is  a  deviation  of  9  cm.,  which,  figured  out  on  the  above 
basis,  would  correspond  to  1^^  prism  D. 

The  amount  of  prismatic  power  that  can  be  developed  by 
decentration  is  on  the  basis  of  1  A  for  every  1  D.  when  de- 
centered  10  mm.,  or  ^  A  for  every  1  D.  when  decentered  5  mm., 
or  1  W  A  for  this  3  D.  lens  when  decentered  5  mm. 


Practical  Optometry  179 

The  rough  lens  would  not  be  large  enough  to  permit  of  this 
decentration  in  the  horizontal  meridian,  but  it  can  be  done  in 
the  vertical  meridian,  which  is  9  mm.  less  than  the  horizontal. 

As  the  right  eye  image  is  lower  than  the  left  the  case  is  one 
of  right  hyperphoria,  which  is  to  be  corrected  by  prism  base 
down  right  eye,  or  base  up  left  eye. 

As  this  is  a  concave  lens  the  base  of  prism  is  opposite  to 
the  direction  of  decentration,  as  the  preferable  direction  for  base 
of  prism  is  up,  as  it  is  customary  to  place  the  prism  over  the  left 
eye  (unless  the  right  eye  is  decidedly  the  poorer  eye),  and  as  it 
is  desired  to  avoid  prisms  in  order  to  incur  the  least  cost,  we  will 
order 

O.  D.  -  3  D.  sph. 

O.  S.    —  3  D.  sph.  decentered  down  5  mm. 


What  are  the  points  of  resemblance  and  difference  between  a 
case  of  spasm  of  the  accommodation  and  a  case  of  myopia.^  In 
what  kind  and  ivhat  degree  of  ametropia  does  spasm  of  the  accom- 
modation generally  occur? 

The  points  of  resemblance  are  that  in  both  conditions  the 
reading  point  is  closer  than  normal,  and  the  acuteness  of  vision 
is  impaired,  which  is  improved  by  concave  lenses. 

The  points  of  difference  are: 

(1)  In  spasm  the  distance  of  the  far  point  does  not  corre- 
spond to  the  degree  of  defect  as  it  does  in  myopia. 

(2)  In  spasm  the  visual  acuity  is  constantly  varying,  while 
in  myopia  it  is  more  likely  to  be  a  fixed  quantity  either  with  the 
naked  eye  or  with  the  correcting  lenses. 

(3)  In  spasm  there  are  complaints  of  pain  and  inability 
to  use  the  eyes  continuously  for  near  work,  while  in  myopia 
there  are  no  asthenopic  symptoms. 

(4)  In  spasm  the  near  point  is  apt  to  be  closer  to  the  eyes 
for  a  given  degree  of  false  myopia  than  for  a  similar  degree  of 
real  myopia. 

(5)  In  spasm  the  distant  vision  is  better  than  the  near, 
while  in  myopia  the  near  vision  is  better  than  the  distant. 


What  is  presbyopia  due  to  and  hoiv  does  it  differ  from  acquired 
hypermetropia? 


180  State  Board  Examinations 

Presbyopia  is  due  to  an  inability  to  accommodate  sufficiently 
to  make  near  vision  clear,  on  account  of  the  sclerosis  of  the 
crystalline  lens  which  comes  on  with  age  and  becomes  noticeable 
in  the  early  40's  only  when  near  vision  is  attempted. 

As  the  presbyopic  changes  progress  there  comes  a  time  late 
in  life  when  distant  vision  also  becomes  impaired  as  a  result  of 
the  lessened  refractive  power  of  the  crystalline  and  then  convex 
lenses  are  needed  not  only  for  reading  but  also  for  distance,  the 
latter  being  weaker  than  the  former.  This  condition  is  known 
as  acquired  hypermetropia. 


What  is  meant  by  mixed  astigmatism?  Describe  the  best 
method  of  testing  such  a  case  and  what  directions  you  would  give  as 
to  the  wearing  of  glasses. 

Mixed  astigmatism  is  that  condition  in  which  the  focal  line 
of  one  meridian  lies  in  front  of  the  retina  and  of  the  other  meridian 
back  of  the  retina;  or  in  other  words,  one  meridian  is  myopic 
and  the  other  hypermetropic. 

The  best  method  of  subjective  testing  is  (after  having  used 
the  ophthalmometer  and  determining  the  presence  of  astigma- 
tism and  the  location  of  the  principal  meridians)  to  correct  the 
hypermetropic  meridian  by  means  of  convex  cylinders,  which 
should  be  crowded  on  to  the  limit  of  acceptance  and  which  will 
not  affect  the  other  meridian,  and  then  use  concave  cylinders  over 
the  convex  cylinder  with  their  axes  at  right  angles.  The  convex 
cylinder  will  advance  the  focus  of  the  hypermetropic  meridian 
to  the  retina,  and  the  concave  cylinder  will  throw  the  focus  of 
the  myopic  meridian  back  to  the  retina,  so  that  the  image  will 
now  be  composed  of  focal  points  on  the  retina  instead  of  focal 
lines  in  front  and  back  of  it. 

The  cross  cylinder  thus  obtained  can  usually  with  advantage 
be  transposed  into  a  sphero-cylinder,  in  which  case  it  is  sometimes 
desirable  to  slightly  reduce  the  convex  element  of  the  combination 
in  order  to  make  them  more  acceptable  to  the  patient. 

The  same  principle  can  be  used  in  the  retinoscopic  test. 
After  having  determined  the  directions  of  the  two  principal  merid- 
ians the  hypermetropic  is  neutralized  by  a  convex  sphere  and  the 
myopic  meridian  by  a  concave  sphere,  from  which,  after  making 
the  necessary  allowances,  the  correcting  combination  can  be  de- 


Practical  Optometry  181 

duced,  remembering  that  the  axis  must  be  placed  at  right  angles 
to  the  meridian. 

In  mixed  astigmatism  the  glasses  should  be  worn  constantly 
and  care  should  be  taken  that  the  glasses  are  kept  in  proper 
adjustment  and  without  displacement  of  the  axes,  which  in  the 
higher  degrees  of  mixed  astigmatism  would  result  in  impairment 
of  vision  and  asthenopic  symptoms. 


If  a  patient  has  myopic  astigmatism,  in  what  case  would  plus 
cylinder  be  prescribed? 

In  a  case  of  simple  myopic  astigmatism,  convex  cylinders 
could  not  be  prescribed  unless  combined  with  the  same  number 
concave  sphere,  but  this  would  increase  the  cost. 

In  compound  myopic  astigmatism  the  transposition  may  be 
made  in  order  to  get  a  higher  concave  surface  and  thus  make  a 
periscopic  effect,  or  to  change  the  axis  from  horizontal  to  vertical, 
or  for  both  purposes. 

For  instance: 

-3D.  sph.  C   -  2  D.  cyl.  axis  180° 
may  be  transposed  to 

-  5  D.  sph.  C   +  2  D.  cyl.  axis  90°, 
with  the  gain  of  both  of  the  above-mentioned  advantages. 


//  a  person  requires  plus  5  D.  in  the  vertical  meridian  aiid  plus 

4  D.  in  the  horizontal  and  is  tested  with  a  small  astigmatic  clock 
dial,  what  would  be  the  farthest  distance  at  which  the  vertical  line 
could  be  distinctly  seen;  also  the  horizontal  lines,  with  a  plus  8  D. 
lens? 

If  the  vertical  meridian  is  hypermetropic  to  the  extent  of 

5  D.  and  a  +  8  D.  lens  is  placed  before  it,  there  is  an  overcor- 
rection of  3  D.,  thus  producing  an  artificial  myopia  of  like  amount, 
with  a  far  point  for  this  meridian  of  13  inches.  And  as  the  hori- 
zontal lines  are  seen  by  the  vertical  meridian  of  the  eye,  therefore, 
13  inches  would  be  the  farthest  distance  at  which  the  horizontal 
lines  could  be  distinctly  seen. 

If  the  horizontal  meridian  is  hypermetropic  4  D.,  and  a  -f  8 
D.  lens  is  placed  before  it,  there  is  an  overcorrection  of  4  D.  with 


182  Slate  Board  Examinations 

an  artificial  myopia  of  like  amount  and  a  far  point  of  10  inches. 
And  as  the  vertical  lines  are  seen  by  the  horizontal  meridian  10 
inches  would  be  the  farthest  point  at  which  the  vertical  lines 
could  be  seen. 

What  change  hi  adjustment  must  be  made  ivhen  a  myope  looks 
through  a  pair  of  field  glasses  just  used  by  an  emmetrope? 

The  tube  must  be  shortened  in  order  to  make  the  emergent 
rays  divergent  and  thus  be  able  to  focus  on  the  retina  of  the 
myopic  eye. 

What  is  the  prismatic  effect  in  a  pair  of  glasses  set  ?w  a  frame 
5  mm.  too  wide  zvhen  the  prescription  is  as  follows: 
R.  E.  +  2.50  Z:   -  1  cyl.  axis  90 
L.  E.  +  3.50  C   -  1.50  cyl.  axis  90 

The  prismatic  effect  is  produced  by  a  decentration  in  the 
horizontal  meridian,  the  power  of  which  is  reduced  in  both  lenses 
by  the  concave  cylinders  to  1.50  D.  in  right  and  2  D.  in  left  eye. 

The  rule  is  lA  of  prismatic  power  for  every  diopter  when 
decentered  10  mm.  In  this  case  where  the  frame  is  5  mm.  too 
wide  there  is  2.5  mm.  decentration  for  each  eye,  which  according 
to  the  above  rule  would  yield  yi/\  for  right  eye  and  >2  A  for  left 
eye,  or  a  total  for  the  two  eyes  of  J^i/\  of  prismatic  effect. 


The  following  is  a  prescription  in  which  the  correction  for  the 
right  eye  is  omitted.    Supply  it: 

Distance  R.  E.  -  0.50  -  1.00  cyl.  axis  45°. 
Distance  L.  E.  missing. 
Near  R.  E.  +  0.50  C  +  1-00  cyl.  axis  135. 
Near  L.  E.  +  3.50  C   —  0.75  cyl.  axis  135. 

A  comparison  of  the  distance  and  near  corrections  of  the 
right  eye  shows  the  addition  of  a  +  2  D.  and  a  transposition  of 
the  cylinder  from  concave  to  convex. 

Assuming  that  the  same  addition  was  made  in  the  near  glass 
of  the  left  eye,  we  must  deduct  this  2  D.,  which  would  leave 

+  1.50  D.  S.  -  .75  D.  cyl.  axis  135° 
or  by  transposition  in  order  to  correspond  with  right  eye 
+  .75  D.  S.  +  .75  D.  cyl.  axis  45° 


Practical  Optometry  183 

What  advantage  is  secured  by  using  the  Maddox  rod  test  as  a 
phorometric  test? 

The  principal  advantage  of  the  Maddox  rod  is  that  its  image, 
although  distorted  and  elongated  into  a  streak,  is  formed  upon 
the  macula;  whereas  in  the  prism  test  the  images  are  displaced 
from  the  macula. 


What  errors  of  refraction  may  be  congenital  and  which  ones 
acquired? 

Usually  we  regard  hypermetropic  errors  as  congenital  and 
myopic  as  acquired. 

What  is  asthenopia? 

The  word  means  weak  sight  and  is  used  in  connection  with  a 
condition  where  the  eyes  can  be  used  but  for  a  short  time,  and  is 
accompanied  by  more  or  less  discomfort,  due  to  strain  of  either 
the  accommodation  or  convergence. 


Describe  a  test  of  the  extrinsic  muscles  which  is  dynamic;  that 
is,  the  test  must  be  made  with  convergence  in  full  action. 

Ask  the  person  being  examined  to  look  at  the  point  of  a  pencil 
which  is  held  in  the  median  line  a  short  distance  in  front  of  the 
face  and  gradually  moved  nearer  to  the  eyes  until  one  of  them 
is  seen  to  abandon  the  effort  of  convergence  and  deviate  from 
the  fixation  point  and  turn  outward.  The  position  of  the  pencil 
when  this  occurs  indicates  the  near  point  of  convergence.  This 
has  been  estimated  to  be  normally  about  four  inches  from  eyes. 


Describe  a  test  of  the  extrinsic  muscles  of  the  eyes  that  is  not 
dynamic;  that  is,  the  test  is  not  made  with  convergence  in  ftdl  force. 

Any  test  that  is  made  with  a  distant  point  of  fixation,  as  for 
instance  the  Maddox  rod  test  with  the  light  20  feet  away.  This 
is  a  test  that  is  "not  dynamic"  because  there  is  no  impulse  to  the 
convergence  for  the  maintenance  of  binocular  vision. 


1 84  State  Board  Examinations 

In  an  astigmatic  eye  where  would  be  the  circle  of  least  diffusion? 

In  astigmatism  the  two  principal  meridians  each  have  a 
different  focus,  the  space  between  which  is  known  as  the  focal 
interval  of  Sturm.  No  matter  what  the  position  of  the  retina 
in  such  an  eye,  no  distinct  image  can  be  formed  upon  it. 

If  it  is  in  focus  for  one  meridian  it  is  very  much  out  of  focus 
for  the  other.  The  accommodation  is  brought  into  action  to  lessen 
as  much  as  possible  the  diffusion  circles,  but  there  can  be  no  true 
focus  for  both  meridians  at  the  same  time,  and  therefore  the  image 
cannot  be  sharp  and  distinct.  Probably  the  best  vision  or  least 
diffusion  would  be  midway  between  the  foci  of  the  two  meridians. 


Why  are  prisms  placed  bases  in  and  out,  respectively,  in 
convergent  and  divergent  strabismus? 

Ordinarily,  strabismus  is  beyond  the  reach  of  prisms,  but 
if  correctible  by  prisms  the  rule  is  to  place  the  base  opposite  to 
deviation,  that  is,  in  convergent  strabismus,  base  out,  and  in 
divergent  strabismus,  base  in.  These  are  the  positions  of  relief 
and  assistance. 

But  if  it  is  desired  to  de\'elop  and  strengthen  a  set  of  muscles 
by  prism  exercise,  then  the  apex  of  the  prism  is  placed  over  the 
muscles  which  it  is  desired  to  act  upon,  that  is,  in  the  positions 
named  in  the  question.  In  convergent  strabismus,  where  it  is 
desired  to  exercise  the  external  recti,  the  prism  is  placed  apex 
out  or  base  in;  in  divergent  strabismus,  where  the  internal  recti 
need  toning  up,  the  prism  is  placed  apex  in  or  base  out. 


In  a  young  person  with  1  diopter  of  hyperopia  the  pinhole 
disk  makes  the  letters  on  the  chart  worse  than  when  seen  with  the 
naked  eye,  while  in  a  myope  of  1  diopter  there  will  be  an  improve- 
ment with  this  test.     What  is  the  reason? 

The  pinhole  test  is  one  that  is  of  value  only  when  vision  is 
impaired.  In  the  case  of  a  young  person  with  1  D.  of  hyper- 
metropia  the  visual  acuity  is  not  lessened  because  the  accom- 
modation instinctively  neutralizes  the  deficient  refraction.  As 
the  vision  is  already  normal  the  pinhole  disk  cannot  make  it 


Practical  Optometry  185 

any  better,  but  rather  makes  it  worse  because  it  cuts  off  so 
much  light  that  would  otherwise  enter  the  eye. 

Whereas,  in  the  case  of  a  myope  of  1  D.  the  acuteness  of 
vision  is  much  impaired  (probably  one-half  normal),  but  it  is  at 
once  raised  to  normal  by  the  pinhole  disk,  for  the  following  reason : 

The  pinhole  allows  the  passage  of  a  very  narrow  pencil  of 
light  and  to  that  extent  diminishes  the  size  of  the  diffusion  circles 
on  the  retina.  If  the  pinhole  be  1  5  the  size  of  the  pupil,  the 
diffusion  circle  on  the  retina  will  be  only  1  5  the  size  of  the 
usual  diffusion  circle. 

Suppose  the  diffusion  circle  upon  the  retina  covered  an  area 
of  100  cones;  with  a  pinhole  15  the  diameter  of  the  pupil  the 
area  will  be  reduced  1  25,  and  only  4  cones  be  covered;  this  will 
result  in  an  enormous  increase  in  the  visual  acuity. 


In  a  case  of  hypermetropia  of  6  diopters  with  little  accommoda- 
tion how  would  we  measure  the  amount  of  facultative  hypermetropia? 

By  the  proportion  of  the  total  hypermetropia  that  can  be 
overcome  by  the  accommodation.  If  this  case  of  6  D.  of  hyper- 
metropia was  fifty  years  of  age  he  would  possess  about  2.50  D. 
of  accommodation,  which  would  be  used  as  far  as  it  would  go 
in  the  correction  of  the  defect,  and  the  balance  must  be  corrected 
by  lenses. 

In  this  case  there  would  be  2.50  D.  of  facultative  and  3.50 
D.  of  absolute  hypermetropia.  The  facultative  is  the  difference 
between  the  total  defect  and  the  weakest  lens  that  raises  vision 
to  normal. 


How  would  you  get  the  amplitude  of  the  convergence-accom- 
modative function? 

By  measuring  the  closest  point  at  which  it  is  possible  to  see 
clearly  and  at  the  same  time  that  binocular  vision  can  be  main- 
tained. The  accommodation  is  expressed  in  diopters  and  the 
convergence  in  meter  angles. 

In  the  emmetropic  eye  an  object  situated  at  8  inches  would 
call  for  5  D.  of  accommodation  and  5  meter  angles  of  convergence. 


186  State  Board  Examinations 

In  ivhat  way  can  eye  zcith  irregular  astigmatism  be  best  cor- 
rected? 

The  center  of  the  cornea  may  be  flatter  or  more  convex, 
thus  gixing  it  a  difi^erent  refractive  power  from  the  periphery; 
or  the  cornea  may  be  studded  with  numerous  facets,  the  results  of 
pre\  ious  ulcers;  in  either  case  vision  is  impaired  and  objects 
distorted. 

It  is  obvious  that  such  a  condition  is  not  correctible  by  the 
usual  forms  of  lenses.  The  only  method  of  improving  vision 
is  to  cut  off^  the  peripheral  rays  and  allow  light  to  pass  through 
a  small  portion  of  the  cornea,  where  the  curvature  is  most  ev^en 
and  the  transparency  greatest.  This  can  be  accomplished  by  an 
opaque  diaphragm  with  a  small  opening  placed  before  the  cornea 
in  the  position  that  is  found  the  most  favorable. 


The  distance  correction  is 

0.  D.  -\-  2  D.  sph.  O.  S.  -  1  D.  sph. 

What  decentration  must  be  given  to  the  added  wafers  of  +  Z.50  D. 
for  reading  in  order  to  neutralize  the  prismatic  effects  which  would 
otherwise  be  produced  by  looking  through  the  centers  of  the  loiver 
fields,  10  mm.  below  the  centers  of  the  distance  lenses? 

On  account  of  the  size  of  the  finished  lenses  it  would  be 
utterly  impossible  to  obtain  a  decentration  of  10  mm.;  with  this 
pro\iso  we  will  answer  the  question  as  it  is  given. 

The  decentration  for  the  two  wafers  will  not  be  the  same 
because  the  distance  lenses  vary  in  character  and  in  power. 

According  to  the  rule  which  has  already  been  given  on  these 
pages,  the  prism  strength  that  would  be  developed  by  a  down 
decentration  of  10  mm.  of  this  convex  lens  of  2  D.  would  be  2° 
with  base  up.  Therefore,  in  order  to  overcome  this  the  wafer  on 
this  lens  would  have  to  be  decentered  down  to  a  corresponding 
degree,  but  as  the  power  of  this  wafer  is  2.50  D.  the  decentration 
necessary  to  produce  a  2°  prismatic  value  base  down  to  balance 
would  be  only  8  mm. 

In  regard  to  the  left  lens,  which  is  a  concave  lens  of  1  D. 
power  the  decentration  downward  of  10  mm.  would  produce  a 
prism  value  of  1°,  but  in  this  case  with  base  down.     In  order  to 


Practical  Optometry  187 

counterbalance  this  the  decentration  of  the   +   2.50  D.   wafer 
would  have  to  be  up  to  the  extent  of  4  mm. 

In  a  case  of  this  kind  it  would  be  well  also  to  order  the 
segments  decentered  inwards,  or  rather  order  the  pupillary 
distance  of  the  segments  to  less  than  that  of  the  distance  lenses, 
to  allow  for  the  necessary  convergence  and  decrease  of  pupillary 
distance  when  the  eyes  are  used  at  close  range. 


The  nearer  of  a  pair  of  strong  minus  lenses  complains  that 
distant  objects  appear  clear  but  diminished  in  size;  how  may  this 
defect  be  rectified  in  part  at  least  without  altering  the  power  of  the 
lenses? 

By  pushing  the  glasses  as  close  to  the  eyes  as  possible. 


Describe  an  accurate  subjective  method  for  detecting  astigmia 
and  determining  its  character. 

Astigmatism  may  be  detected  subjectively  in  two  ways: 

1.  Use  of  the  card  of  radiating  lines,  and  the  reply  of  the 
patient  that  lines  running  in  one  direction  are  notably  plainer 
and  more  distinct  than  lines  running  in  some  other  directions. 

2.  Use  of  the  card  of  test  letters  and  the  acceptance  by  the 
patient  of  the  cylinder  as  affording  better  vision  than  a  sphere. 

The  character  of  the  astigmatism  is  determined  in  each  case 
by  the  lenses  required.  If  convex  are  accepted,  hypermetropic; 
if  concave  are  required,  myopic. 


A  child  in  good  health  shows  under  objective  test  by  the  static 
method  5  D.  of  hyperopia  and  with  the  Maddox  rod  test  or  a  similar 
test  esophoria  of  8  degrees,  what  correction  would  you  prescribe? 

The  fact  that  hypermetropia  and  esophoria  exist  together 
shows  that  the  functions  of  accommodation  and  convergence 
maintain  their  proper  relation  to  each  other.  Under  such  cir- 
cumstances we  are  usually  justified  in  giving  the  full  correction 
for  the  refractive  error.  Whether  or  not  we  would  prescribe  exactly 
the  +  5  D.  would  depend  upon  the  age  of  the  patient  and  the 
effect  of  the  lenses  on  the  acuteness  of  vision.  If  the  child  was 
over  6  and  the  acuteness  of  vision  was  markedly  diminished  by  the 


188  State  Board  Examinations 

lenses,  we  might  feel  it  achisahlc  to  reduce  them,  whereas  younger 
children  hear  stronger  lenses  and  possible  blurring  with  little 
complaint. 

Explain  the  uses  of  the  stenopaic  slit  and  the  pinhole  disk  and 
give  the  praetieal  value  of  eaeh. 

The  stenopaic  slit  is  intended  to  restrict  the  rays  of  light 
entering  the  eye  to  one  meridian  and  in  this  way  we  can  study 
the  acuteness  of  vision  and  refraction  of  that  one  particular 
meridian.  When  placed  at  90  degrees  the  vertical  meridian  comes 
under  observation ;  when  at  180  degrees,  the  horizontal.  Its 
special  field  is  in  the  detection  and  correction  of  astigmatism. 

The  stenopaic  slit  is  placed  in  the  Trial  Frame  and  rotated 
through  the  different  meridians,  while  the  patient  looks  at  the 
letters  on  the  test  card.  In  this  way  each  meridian  for  the  moment 
performs  the  act  of  vision,  and  if  there  is  any  difference  in  vision 
in  the  various  meridians,  getting  better  in  one  way  and  getting 
worse  in  the  other,  astigmatism  is  shown  to  be  present.  For 
instance,  when  at  90  degrees  vision  may  be  20/20  and  at  180 
degrees,  20/30.  The  spherical  lens  placed  in  front  of  the  slit  will 
measure  the  refraction  of  each  meridian,  and  the  difference  be- 
tween the  two  lenses  will  show  the  amount  of  astigmatism. 

The  pinhole  disk  is  made  use  of  in  cases  of  greatly  impaired 
vision  to  determine  if  the  trouble  is  due  to  an  error  of  refraction 
or  not.  If  the  pinhole  raises  vision,  then  glasses  will  be  of  bene- 
fit; but  if  it  fails  to  cause  any  improvement  then  there  is  little 
use  to  try  to  prescribe  glasses.  This  is  a  simple  and  practical 
method  to  determine  if  the  impaired  vision  is  due  to  disease  or 
to  refractive  error. 


How  may  it  be  positively  determined  {subjectively)  whether  or 
not  ametropia  is  present  tvhen  vision  is  20/20  ivithout  lenses?  What 
may  be  the  character  of  the  ametropia? 

It  is  possible  for  vision  to  equal  20/20  in  presence  of  hyper- 
metropia  or  slight  hypermetropic  astigmatism  because  the  accom- 
modation is  instinctively  brought  into  action  to  overcome  the 
deficient  refraction  and  maintain  vision  at  the  normal  standard. 
In  such  cases  weak  convex  lenses  may  be  accepted,  but  just  as 


Practical  Optometry  189 

often  they  are  rejected;  the  proper  way  to  positively  determine 
the  presence  of  hypermetropia,  which  may  be  latent,  is  by  means 
of  the  fogging  system. 

A  patient  35  years  of  age  having  3  diopters  of  hypermetropia 
asks  for  "reading'  glasses  but  complains  of  constant  migraine;  give 
the  correction  that  you  ivoiild  order  and  state,  with  reason,  when  in 
your  opinion  the  glasses  should  be  worn. 

The  fact  that  the  patient  suffers  with  constant  headache 
would  be  sufficient  reason  for  advising  glasses  to  be  worn  con- 
stantly. We  do  not  know  what  method  was  used  to  measure  the 
3  D.  of  hypermetropia,  nor  what  the  acuteness  of  vision  was 
naturally  and  with  glasses.  Perhaps  the  patient  will  not  bear 
the  full  correction  for  constant  wear,  in  which  case  we  would  order 
as  strong  as  can  be  comfortably  worn  for  that  purpose,  and  the 
+  3  D.  as  an  additional  pair  for  reading.  As  patient  will  probably 
object  to  two  pairs  of  glasses,  we  would  theoretically  be  justified 
in  ordering  the  +  3  D.  for  constant  wear  and  also  for  reading,  but 
in  practice  we  are  sometimes  compelled  to  modify  as  above. 


//  there  is  a  tendency  of  the  eyes  to  cross,  on  which  side  will  the 
light  streak  appear  with  the  Maddox  rod  over  the  left  eye?  How  should 
the  prism  be  placed  to  bring  the  lights  together? 

By  "tendency  of  the  eyes  to  cross"  we  understand  a  tendency 
to  convergent  strabismus;  this  would  result  in  homonymous 
diplopia,  in  which  right  image  belongs  to  right  eye  and  left  image 
to  left  eye. 

With  Maddox  rod  over  left  eye,  the  streak  of  light  would 
appear  to  the  left;  this  is  corrected  by  prism  placed  base  out, 
because  prisms  displace  objects  toward  their  apex. 


State  (a)  how  the  amplitude  of  accommodation  is  measured, 
(b)  how  convergence  is  measured. 

(a)  The  nearest  point  for  which  the  eye  can  accommodate 
by  the  strongest  effort  of  the  ciliary  muscle  represents  the  ampli- 
tude  of  accommodation.     As  explained   above,   if   this  should 


190  Sidle  Board  Examinations 

be  5  inches,  then  8  I),  is  the  measure  of  the  aniplitiule  of  accom- 
modation;  if  at  4  inches,  then  10  D.  of  accommodation. 

(b)  The  degree  of  convergence  is  measured  by  the  angle 
through  which  each  eye  must  turn  from  parallelism  of  the  visual 
lines  in  order  to  converge  to  the  near  point  of  fixation.  The  ampli- 
tude of  convergence  is  the  distance  from  the  far  point  to  the  near 
point  of  convergence,  and  is  expressed  by  the  greatest  number  of 
meter  angles  which  the  eyes  can  exert,  the  meter  angle  being 
that  angle  through  which  the  eyes  must  turn  from  parallelism 
to  converge  at  a  point  one  meter  away.  At  20  inches  (>^  meter) 
there  would  be  2  meter  angles  of  convergence;  at  10  (>^  meter) 
4  meter  angles,  and  so  on.  In  emmetropia  the  convergence  and 
accommodation  are  equal;  for  instance,  at  10  inches  there  are 
4  meter  angles  of  convergence  and  4  D.  of  accommodation. 

The  convergence  can  also  be  measured  by  the  strongest 
prisms,  bases  out,  which  the  eyes  are  able  to  overcome  and 
maintain  single  vision. 

Give  reasons  for  and  against  full  correction  of  myopia  (a)  in 
orthophoria,  {b)  in  heterophoria. 

(a)  When  orthoporia  exists  in  connection  with  myopia,  the 
indications  would  be  against  the  full  correction  of  the  refractive 
error,  all  other  things  being  equal,  because  the  normal  relation 
between  accommodation  and  convergence  has  not  been  main- 
tained. 

{h)  If  esophoria  exists  in  connection  with  myopia,  the  indi- 
cations are  still  stronger  against  the  full  correction  of  the  refrac- 
tive error,  because  the  relations  between  it  and  the  muscle  balance 
are  just  the  reverse  of  what  they  should  be. 

When  exophoria  exists  in  connection  with  myopia,  full  cor- 
rection of  the  latter  is  indicated,  because  the  relations  are  normal, 
and  the  concave  lens  also  corrects  the  tendency  to  outward  devia- 
tion. 

//  an  addition  to  the  prescription  for  distance  glasses  must  be 
made  for  presbyopia  of  +  3.50  D.  or  more,  what  error  in  the  prescrip- 
tion for  distance  should  be  suspected? 

For  the  correction  of  simple  and  uncomplicated  presbyopia, 
glasses  are  seldom  required  stronger  than  +  3  D.  Therefore,  in 


Practical  Optometry  191 

the  case  mentioned  where  +  3.50  D.  or  more  must  be  added  for 
reading,  it  is  fair  to  assume  that  the  hypermetropia  has  not  been 
fully  corrected  and  that  the  distance  glasses  are  not  as  strong  as 
they  should  be. 


State  {not  describe)  the  various  methods  yon  n'ould  employ  in 
making  a  thorough  examination  of  the  eyes.  Write  a  hypothetic 
prescription  involving  sphero-cylinder  prisms  in  bifocal  form  and 
give  a  complete  case  record  of  the  same. 

Acuteness  of  ^•ision. 

Amplitude  of  accommodation. 

Ophthalmometer. 

Ophthalmoscope. 

Retinoscope. 

Trial  case  examination. 

Muscle  tests. 

O.  D.  =  20  60  -  1  D.  sph.  -  50  D.  cyl.  axis  180°  =  20/20. 

O.  S.  =  20  40  -  50  D.  sph.  -  50  D.  cyl.  axis  180°  =  20/20. 

Reads  .50  D.  type,  10"  to  30". 

Ophthalmometer  shows  .50  D.  excess  in  vertical  meridian. 

Ophthalmoscope,  normal  fundus. 

Retinoscope,  against  movement. 

R.  E.,  —  1  horizontally,  —  1.50  vertically. 

L.  E.,  —  .50  horizontally,  —  1  vertically. 

Maddox  rod  =  4°  exophoria. 

Prescription  given  as  follows: 

O.  D.,  -  1  D.  sph.  -  .50  D.  cyl.  axis  180°  C  Pr.  1°  b.  in. 

O.  S.,  -  .50  D.  sph.  -  .50  D.  cyl.  axis  180°  C  Pr.  1°  b.  in. 

+  1.50  D.  segments  added. 


After  fogging  the  vision  ivith  plus  lenses  how  do  you  proceed  and 
when  do  you  stop? 

Proceed  to  neutralize  the  excessive  convexity  and  reduce  the 
fogging  by  means  of  concave  lenses  placed  in  front  of  the  fogging 
lens  and  gradually  increased  until  a  vision  of  20/20  is  reached. 
We  must  stop  here  or  the  purpose  of  the  fogging  system  would  be 


192  State  Board  Examinations 

defeated.    Stronger  concaves  would  be  accepted  if  used  but  they 
must  not  be  tried. 

About  how  much  difference  can  be  made  in  glasses  when  the 
eyes  are  not  alike  in  fociisj' 

If  a  rule  must  be  given  we  would  say  from  1.50  D.  to  2  D., 
but  there  is  a  wide  difference  of  opinion  on  this  point.  The  writer 
has  had  cases  where  a  difference  of  4  D.  and  5  D.  has  been  made. 
After  all  it  is  a  matter  that  must  be  left  to  experience  in  each 
individual  case.  The  effort  should  always  be  made  to  give  each 
eye  its  own  proper  correction.  If  such  a  difference  proves  uncom- 
fortable then  the  glass  of  the  poorer  eye  must  be  changed  but  only 
so  much  as  to  make  it  bearable. 


Do  you  prescribe  the  weakest  or  strongest  lens  with  which  a 
patient  can  see  20/20  in  hypermetropia  and  why? 

We  give  preference  to  the  stronger  glass  in  order  to  relieve 
the  unnatural  tax  upon  the  accommodation  and  because  the 
strongest  convex  lens  is  the  measure  of  the  manifest  hyperme- 
tropia only  and  there  is  usually  some  latent  error  back  of  it  which 
is  not  discovered  by  any  lens. 


In  myopia?    Why? 

In  myopia  we  give  preference  to  the  weakest  glass  in  order 
to  lessen  the  tax  upon  the  accommodation  and  because  there  is 
usually  some  spasm  of  the  ciliary  muscle,  which  makes  the  myopia 
appear  greater  than  it  actually  is  and  thus  leads  to  the  choice  of 
a  concave  glass  that  is  stronger  than  enough  to  correct  the  real 
amount  of  myopia. 

What  is  presbyopia  and  how  corrected? 

Presbyopia  is  that  condition  of  vision  where  on  account  of  a 
failure  of  accommodation,  due  to  a  loss  of  contractility  of  the 
ciliary  muscle  and  of  elasticity  of  the  crystalline  lens,  the  near 
point  recedes  to  an  inconvenient  distance  and  reading  is  impaired 
or  made  impossible. 


Practical  Optometry  193 

It  is  corrected  by  means  of  a  convex  lens,  which  restores  the 
receded  near  point,  assists  the  accommodation  and  places  in  front 
of  the  eye  the  necessary  convexity  which  has  been  lost  within  it. 


How  do  you  test  the  external  and  internal  muscles? 

By  prisms,  with  apex  over  the  muscle  it  is  desired  to  test. 


How  many  degrees  of  prism,  base  out,  should  a  person  overcome? 
20°  to  30°. 


How  many  degrees  of  prism  should  a  person  overcome  base  in? 
Up  or  down? 

6°  to  8°  base  in. 

2°  to  3°  up  or  down. 


//  the  eyes  turn  in,  how  do  you  place  the  base  of  a  prism? 
Out,  the  rule  being  base  opposite  to  deviation. 


What  is  the  object  of  fogging  with  strong  plus  lenses? 

To  encourage  relaxation  of  the  ciliary  muscle  and  reduce 
spasm  of  the  accommodation. 


How  do  you  test  for  astigmatism? 

Objectively  by  the  ophthalmometer  and  the  retinoscope  and 
subjectively  by  the  radiating  lines  and  cylindrical  lenses. 


How  would  you  use  the  stenopaic  slit  in  finding  the  error  of 
refraction  in  an  eye  which  has  astigmatism? 

The  stenopaic  slit  is  placed  in  position  before  the  eye  of 
the  patient,  who  is  asked  to  look  at  the  test  letters.  It  is  then 
rotated  to  that  place  where  the  letters  are  seen  the  plainest,  which 
will  be  one  of  the  principal  meridians  and  that  of  best  vision. 


194  State  Board  Examinations 

The  meridian  at  right  angles  will  be  the  other  principal 
meridian  and  that  of  poorest  vision.  The  refraction  of  each 
meridian  is  measured  by  spherical  lenses. 

If  the  vision  in  the  first  meridian  is  normal,  this  meridian 
may  be  emmetropic  or  hypermetropic.  The  vision  in  the  second 
meridian  is  necessarily  below  normal,  and  may  be  hypermetropic 
or  myopic. 

Convex  lenses  are  tried  in  the  first  meridian;  if  rejected  we 
assume  this  meridian  is  normal  and  the  case  one  of  simple  astig- 
matism. If  accepted,  this  meridian  is  hypermetropic  and  the 
astigmatism  is  either  compound  or  mixed. 

The  second  meridian  is  measured  by  convex  and  concave 
lenses  in  the  usual  way.  If  convex  lenses  (of  different  strengths) 
are  accepted  in  both  meridians,  the  astigmatism  is  compound ;  if 
convex  lenses  in  one  meridian  and  concave  in  the  other,  mixed. 

It  must  be  remembered  that  the  axis  of  the  correcting  cylinder 
is  to  be  placed  at  right  angles  to  the  meridian  that  is  being 
measured.  For  instance,  if  +  .50  D.  is  accepted  in  the  vertical 
meridian,  the  correcting  lens  would  be  +  -50  D.  cyl.  axis  180°. 

If  +  1  D.  is  accepted  in  the  horizontal  meridian,  the  cor- 
recting lens  would  be  +  1  D.  cyl.  axis  90°. 

And  the  prescription  would  be  -f-  .50  D.  sph.  O  +  -50  D. 
cyl.  axis  90°. 


What  is  understood  by  the  so-called  "cover"  and  "fixation" 
tests  for  muscular  weaknesses? 

In  any  case  of  muscular  weakness  we  assume  the  good  eye 
to  be  the  fixing  eye.  The  patient  is  asked  to  look  at  an  object 
some  distance,  a  light  being  the  best.  A  card  is  then  placed  over 
the  fixing  eye,  thus  excluding  it  from,  vision,  when  the  patient 
will  be  compelled  to  use  his  other  eye  to  see  the  light.  If  this 
causes  any  movement  in  either  eye  there  is  evidence  of  muscular 
insufficiency.  Both  eyes  should  be  covered  in  turn,  and  if  there 
is  no  movement  of  either  eye  after  covering  or  uncovering,  both 
eyes  would  seem  to  fix,  thus  contraindicating  insufficiency. 

If  either  eye  turns  inward  when  its  fellow  is  covered,  it 
must  previously  have  been  deviating  outwards;  and  if  the  excur- 
sion should  be  outward,  the  previous  deviation  must  have  been 
inward. 


Practical  Optometry  195 

In  the  fixation  test  both  eyes  look  at  an  object,  the  distance 
of  which  is  quickly  changed,  while  the  corresponding  mov^ements 
of  the  two  eyes  are  closely  watched,  according  to  which  we  can 
detect  the  presence  of  insufficiency. 


What  test  may  be  applied  to  determine  whether  or  not  an 
anisometrope  will  accept  his  full  correction  for  widely  different 
states  of  refraction? 

There  is  no  definite  test  at  our  command  by  which  we  can 
determine  this  point.  It  is  a  matter  that  really  can  be  decided 
only  by  the  experience  of  the  patient.  The  glasses  should  be 
tried  for  ten  or  fifteen  minutes  in  the  office,  and  if  there  is  no 
decided  objection  they  may  be  given  tentatively  for  a  few  days' 
or  a  few  weeks'  wear.  If  there  is  a  slight  discomfort  at  first, 
this  may  pass  away  after  a  few  days  wearing  of  the  glasses. 
At  any  rate  a  reasonable  efTort  must  be  made  to  have  the  eyes 
bear  the  full  correction  for  each  eye. 


What  do  you  consider  the  most  satisfactory  way  of  correcting 
high  myopia;  full  correction  or  partial  correction? 

This  depends  upon  a  great  many  circumstances,  such  as  age, 
amplitude  of  accommodation,  whether  glasses  had  been  pre- 
viously worn,  and  if  so,  the  proportion  of  full  correction  and  the 
character  of  the  work  for  which  the  eyes  are  to  be  used,  as  well 
as  the  degree  of  defect  and  the  amount  of  vision  obtainable. 

When  patient  first  puts  on  glasses  it  is  best  to  start  with  an 
undercorrection,  which  may  be  increased  from  time  to  time  until 
the  full  correction  is  reached  for  distance.  But  for  close  use 
glasses  2  D.  to  3  D.  weaker  should  be  used. 

It  is  understood  that  the  stronger  the  concave  lenses  the 
greater  the  tax  upon  the  accommodation,  and  as  this  function  is 
less  developed  in  myopia,  caution  must  be  observed  not  to 
increase  this  tax  to  the  point  of  causing  asthenopia.  On  the 
other  hand,  it  may  be  possible  to  contribute  to  the  ciliary  in- 
sufficiency by  weak  lenses,  or  to  develop  the  strength  of  the 
accommodation  by  lenses  that  are  purposely  made  stronger  for 
that  purpose. 


196  State  Board  Examinations  ^ 

Name  and  describe  the  two  principal  divisions  of  hyperme- 
tropia. 

Hypermetropia  as  met  with  may  be  divided  into  manifest 
and  latent.  Manifest  is  that  which  is  not  concealed  by  the  ciliary 
muscle,  and  is  determined  by  the  strongest  glass  the  patient  can 
be  induced  to  accept  for  distant  vision.  Latent  hypermetropia  is 
that  which  is  neutralized  by  the  power  of  accommodation,  and 
usually  in  its  entirety  can  be  revealed  only  by  the  action  of  a 
cycloplegic. 

The  manifest  error  may  vary  from  time  to  time  according 
to  the  tonicity  of  the  ciliary  muscle.  In  youth  the  manifest  is 
proportionately  small  and  the  latent  correspondingly  large.  With 
the  advance  of  years  the  manifest  increases  at  the  expense  of  the 
latent,  until  finally  the  defect  is  all  manifest.  This  condition  is 
then  known  as  absolute  hypermetropia,  when  vision  becomes 
impaired  and  convex  lenses  are  a  necessity. 


Explain  the  states  of  vision  that  should  govern  the  decision  as 
to  whether  or  not  lenses  should  he  worn  constantly. 

Theoretically,  all  errors  of  refraction  call  for  constant 
wearing  of  glasses,  but  this  is  particularly  true  of  hypermetropia 
and  hypermetropic  astigmatism;  and  yet  even  here  in  slight 
degrees  of  defect  in  the  presence  of  a  vigorous  accommodation 
there  may  be  exceptions  to  this  rule.  In  mild  cases  of  myopia 
where  the  distant  vision  is  not  inconveniently  impaired,  the 
constant  wearing  of  glasses  may  be  considered  as  much  a  luxury 
as  a  necessity. 

Independent  of  the  condition  of  vision,  and  even  when 
vision  is  normal,  there  are  many  cases  that  require  the  constant 
wearing  of  glasses  to  relieve  the  strain. 


Describe  the  methods  of  measuring  the  amplitudes  of  accom- 
modation and  convergence. 

In  order  to  measure  the  amplitude  of  accommodation  the 
patient  is  given  a  card  of  very  fine  print  and  the  very  closest 
point  at  which  it  is  possible  to  read  this  is  measured  in  inches; 


Practical  Optometry  197 

this  is  transposed  into  diopters,  which  will  represent  the  amplitude 
of  accommodation. 

To  measure  the  amplitude  of  convergence  a  pin  may  be 
used  and  the  closest  possible  point  at  which  it  is  seen  singly  will 
be  noted,  and  this  corrected  into  meter  angles. 


What  error  of  refraction  is  often  indicated  on  the  surface  of 
the  cornea? 

Astigmatism. 


What  is  the  condition  called  if  the  right  eye  deviates  upward? 

Right   hyperphoria,    or   if   there   is   actual   and    noticeable 
deviation,  right  hypertropia. 


Name  four  methods  of  detecting  hyperphoria. 

Maddox  rod,  Maddox  double  prism,  phorometer  and  prism 


test. 


What  advice  woidd  you  give  to  a  patient  when  he  first  wears 
glasses? 

This  depends  somewhat  on  the  character  and  degree  of  the 
refractive  error.  In  hypermetropia  and  astigmatism  we  would 
tell  him  the  glasses  may  seem  strange  at  first  and  that  it  will 
take  him  a  little  time  to  get  accustomed  to  them.  We  will 
warn  him  that  the  ground  may  seem  to  slant  as  if  he  were  walking 
up  hill  and  there  may  be  some  distortion  of  objects,  but  that  if 
he  will  persist  in  wearing  the  glasses  for  several  days  these  un- 
pleasantnesses will  most  likely  gradually  pass  away.  In  many 
of  these  cases  the  natural  acuteness  of  vision  is  normal,  hence  in 
order  that  a  patient  may  not  be  disappointed  it  is  well  to  tell 
him  that  the  glasses  are  not  intended  to  make  him  see  better, 
but  to  relieve  the  strain  and  discomfort  from  which  he  suffers. 


In   making   a    rapid   preliminary   examination   what   would 
cause  you  to  suspect  high  myopia? 


198  State  Board  Examinations 

A  great  impiiirment  of  distant  vision,  so  that  even  the  largest 
letters  on  the  test  card  could  not  be  named ;  a  tendency  to  bring 
reading  and  small  objects  very  close  to  the  eyes,  and  a  squinting 
or  half  closing  of  the  lids;  a  dull,  slow  movement  against  the 
mirror  with  the  plane  retinoscope;  a  rejection  of  convex  lenses 
and  a  marked  improvement  in  vision  by  concave  lenses. 


Whejt  ivill  a  hyperope  accept  minus  glasses  for  distance? 

When  there  is  spasm  of  accommodation,  as  there  usually  is 
in  hypermetropia.  If  the  accommodation  was  passive  rays  of 
light  would  strike  the  retina  before  they  could  come  to  a  focus, 
resulting  in  a  blurred  image;  but  as  soon  as  the  eyes  are  opened 
the  accommodation  at  once  comes  into  action  to  increase  the  re- 
fractive power  of  the  hypermetropic  eye  and  bring  the  rays  to  a 
focus  on  the  retina.  It  sometimes  happens  that  this  action,  of 
the  accommodation  is  overdone;  that  is,  more  effort  is  exerted 
than  is  just  necessary  to  neutralize  the  hypermetropia,  and  then 
a  condition  of  false  myopia  is  produced  when  concave  lenses 
would  be  accepted.  It  goes  without  saying  that  even  if  accepted, 
concave  lenses  should  not  be  prescribed  in  hypermetropia. 


What  is  astigmatism? 

That  condition  of  the  eye  where  its  refraction  is  similar  to 
a  sphero-cylindrical  lens,  where  there  are  two  meridians  of 
greatest  and  least  curvature,  the  difference  between  which 
represents  the  amount  of  astigmatism,  and  as  a  result  the  rays 
cannot  be  focussed  at  a  single  point,  but  there  is  a  focus  for  each 
meridian. 

In  the  practice  of  optometry  what  is  sought  to  be  done  by  the 
use  of  lenses? 

To  correct  ametropia  and  heterophoria.  To  add  to  the 
refractive  power  where  deficient,  as  in  hypermetropia;  to  lessen 
the  refractive  power  where  excessive,  as  in  myopia,  and  to 
equalize  the  refraction  in  all  the  meridians  of  the  eye,  when  one 
or  more  are  in  error,  as  in  astigmatism.  In  other  words,  to  make 
the  eyes  emmetropic.      In  heterophoria   to  assist  the  deficient 


Practical  Optometry  199 

muscles  by  prisms  in  position  of  relief  and  thus  restore  the 
proper  equilibrium;  also  to  develop  these  muscles  by  prisms  in 
position  of  exercise.  Tt)  neutralize  any  deficiency  in  accom- 
modation, as  in  presbyopia.  In  fine,  to  improve  vision  or  make 
it  more  comfortable  by  removing  strain. 


In  testing  with  the  stenopaic  slit  it  is  found  that  the  right  eye 
requires  +  1.75  in  the  vertical  meridian  and  —  .75  in  the  horizontal. 
What  is  the  prescription? 

+  1.75  D.  cyl.  ax.  180°  C   -  -75  D.  cyl.  ax.  90° 
This  cross  cylinder  may  be  transposed  into  either  of  the  following 
sphero-cylinders : 

+  1.75  D.  sph.  C   -  2.50  D.  cyl.  axis    90° 
-     .75  D.  sph.  C  +  2.50  D.  cyl.  axis  180° 


What  rule  is  to  he  observed  in  the  giving  of  minus  lenses  in 
myopia? 

When  a  concave  lens  of  the  proper  strength  to  exactly 
neutralize  the  myopia  is  placed  before  such  an  eye, "parallel  rays 
are  diverged  just  enough  to  throw  the  focus  from  in  front  of  the 
retina  back  on  to  the  retina.  If  the  concave  lens  is  any  stronger 
than  necessary  the  rays  are  made  more  divergent,  which  would 
tend  to  cause  them  to  focus  behind  the  retina;  but  the  accom- 
modation instinctively  comes  into  action  to  bring  the  focus  of 
these  divergent  rays  forward  to  the  retina.  This  led  to  the  rule 
that  in  myopia  the  weakest  glasses  that  afford  satisfactory  vision 
should  be  prescribed  in  order  to  avoid  a  tax  upon  the  accom- 
modation. 

It  may  be  argued  that  a  hypermetrope  sees  better  with  a 
glass  that  is  not  a  full  correction  and  which  allows  him  to  use 
some  of  his  accommodation,  and  hence  there  is  no  harm  in  an 
over-correction  of  myopia  where  vision  is  made  perfectly  clear 
by  a  slight  use  of  the  accommodation.  But  it  must  be  remem- 
bered that  the  former  is  accustomed  to  accommodating  and  his 
ciliary  muscle  is  large  and  well  developed,  while  in  the  latter 
case  there  is  but  little  need  for  accommodation  and  the  ciliary 
muscle  is  small  and  weak.     Of  course,  if  glasses  are  placed  in 


200  Stale  Board  Examinations 

youth  on  a  piitient  who  is  vigorous  the  ciHary  muscle  is  Hkely 
to  develop  the  normal  power,  but  if  glasses  are  first  worn  later  in 
life,  or  in  any  case  as  age  creeps  on,  the  glasses  should  be  kept 
weak,  or  reduced  for  close  use. 


What  is  indicated  when  the  pinhole  disk  alone  produces  marked 
improvement  of  vision  ? 

That  the  impairment  of  vision  is  due  to  an  error  of  refraction 
and  that  it  can  be  corrected  by  lenses. 


The  patient  is  directed  to  look  at  a  light  20  feet  distant  and 
is  given  diplopia  with  a  prism,  base  down,  before  the  right  eye;  what 
defect  and  amount  of  error  are  present  when  the  upper  light  is 
located  to  the  left  and  a  prism  of  5°  before  each  eye  is  required  to 
bring  both  lights  to  the  median  line?  What  is  the  position  of  the  5° 
prisms? 

An  artificial  vertical  diplopia  is  produced  by  the  prism  base 
down  before  right  eye.  The  upper  light  will  belong  to  this  eye, 
and  if  it  is  located  to  the  left  a  condition  of  crossed  diplopia  is 
shown  to  be  present,  due  to  an  exophoria.  The  amount  of  the 
imbalance  is  10°  and  the  prisms  are  placed  bases  in. 


A  hyper  ope  of  2.5  D.  sees  ivith  his  right  eye  the  Maddox-rod 
line  6  cm.  higher  than  the  object  light;  write  the  prescription  for 
distance  lenses,  0  eye  size,  so  that  the  least  cost  will  be  incurred. 

Inasmuch  as  the  image  formed  in  the  right  eye  is  the  highest, 
the  condition  is  one  of  left  hyperphoria,  which  can  be  corrected 
by  prism  base  down  left  eye  or  base  up  right  eye.  And  as  it  is 
desired  to  write  a  prescription  incurring  the  least  cost,  it  is 
necessary  to  obtain  this  prismatic  effect  by  a  decentering  of  the 
lenses. 

No  mention  is  made  of  the  distance  at  which  the  test  is 
made,  but  we  will  assume  the  usual  distance  of  20  feet  or  6  meters. 
The  deviation  for  one  prism  diopter  is  just  1  cm.  for  each  meter 
of  distance;  hence  for  6  meters  there  is  6  cm.  of  displacement. 
Therefore,  in  this  instance  where  there  is  6  cm.  of  deviation, 
there  is  indicated  1  p.  d.  of  insufficiency. 


Practical  Optometry  201 

The  rule  for  decentration  is  as  many  degrees  of  prism  power 
as  there  are  diopters  of  refractive  power  for  every  decentration 
of  10  mm.  In  this  case  the  combined  value  of  the  two  lenses  is 
5  D.,  which  would  afford  5°  of  prismatic  power  if  decentered 
10  mm.,  or  1°  prismatic  power  if  decentered  2  mm.  As  this  is 
the  amount  desired,  it  can  be  obtained  by  decentering  the  right 
lens,  2  mm.  up,  or  the  left  lens  2  mm.  down,  or  dividing  the 
decentration  between  the  two  eyes,  right  eye  1  mm.  up  and  left 
eye  1  mm.  down. 

What  are  the  conditions  of  vision  which  make  the  use  of  distance 
glasses  imperative? 

When  the  acuteness  of  vision  is  so  greatly  impaired  by 
marked  degrees  of  myopia,  hypermetropia  or  astigmatism  as  to 
interfere  with  the  ordinary  occupations  of  life,  or  to  make  walking 
in  a  crowded  street  difficult  or  dangerous. 


When  may  distance  glasses  be  dispensed  with? 

Principally  in  hypermetropia  in  the  slighter  degrees  and 
especially  in  young  people  where  the  accommodation  is  active 
and  vigorous,  and  no  symptoms  of  asthenopia  are  in  evidence. 


A  person  aged  40  can  just  see  distant  objects  clearly  with  a 
minus  1.50  D.  lens.  What  glasses,  if  any,  woidd  be  required  for 
reading  at  14  inches?  What  reading  glass  ivould  be  required  at 
double  his  age? 

We  wdll  assume  that  the  —  1 .50  D.  lens  represents  the  amount 
of  myopia  present. 

The  average  amplitude  of  accommodation  at  40  years  of  age 
is  4.50  D.,  which  in  this  case  is  increased  by  the  myopia  to  6  D., 
of  which  he  is  able  to  use  comfortably  from  one-half  to  two-thirds, 
or  3  D.  to  4  D.  At  14  inches  2.75  D.  of  accommodation  is  neces- 
sary, so  that  it  is  evident  there  is  still  a  surplus  of  accommodation 
and  no  glasses  will  be  necessary  for  reading. 

At  80  years  of  age,  when  the  accommodation  is  entirely  lost, 
he  would  theoretically  need  +  1.25  D.  lenses,  which  added  to  the 
1.50  D.  of  myopia  would  give  the  2.75  D.  necessary  for  reading 


202  State  Board  Examinations 

at  14  inches.  But  practically  on  account  of  the  senile  diminution 
of  refractive  power  it  is  likely  the  glasses  will  have  to  be  stronger 
than  1.25  D. 


In  cases  of  esophoria  where  is  the  base  of  the  prism  to  be  placed, 
in  or  out,  and  how  should  strength  or  number  of  prism  be  determined 
for  exercising  the  same,  and  the  proper  way  of  exercising? 

For  the  correction  of  esophoria  the  base  of  the  prism  is  placed 
out. 

If  the  esophoria  was  supposed  to  be  due  to  w^eakness  of  the 
external  recti  and  it  w^as  desired  to  exercise  the  same,  the  apex 
of  the  prism  must  be  placed  over  the  muscle  to  be  exercised,  which 
in  this  case  would  be  base  in. 

First  it  must  be  determined  how  much  these  muscles  are 
able  to  overcome.  Normally  these  muscles  have  a  strength  of  6° 
to  8°.  If  they  were  weak  this  might  be  reduced  to  1°  or  2°,  but 
this  must  be  determined  as  a  starting  point,  and  then  the  strength 
of  the  prisms  gradually  increased  until  the  normal  standard  is 
reached. 

A  certain  patient  is  astigmatic,  presbyopic  and  hypermetropic. 
In  what  order  are  these  defects  tested  for? 

We  examine  for  errors  of  refraction  first  and  of  accommoda- 
tion next.  Of  the  errors  of  refraction  we  commence  with  the 
spherical  errors,  hence  the  order  would  be:  Hypermetropia,  astig- 
matism and  presbyopia. 

//  a  6°  prism  is  placed  in  front  of  an  eye  with  both  eyes  in  use, 
in  what  direction  does  the  base  of  the  prism  have  to  be  in  order  that 
there  might  be  diplopia? 

If  placed  base  out,  it  would  be  quickh^  overcome  by  the 
internal  recti.  If  base  in,  there  is  some  question  whether  it  could 
be  overcome  b}^  the  external  recti,  and  there  might  be  diplopia. 
But  if  placed  vertical  there  would  surely  be  diplopia. 


An  eye  is  hypermetropic  4  D.,  of  which  1  D.  is  latent.  What  will 
be  his  far  point  with  a  ~\-  6  D.  lens? 


Practical  Optometry  203 

If  the  latent  hypermetropia  refused  to  accept  correction  there 
would  be  3  D.  of  manifest  hypermetropia.  Then  the  6  D.  lens 
would  represent  an  overcorrection  of  3  D.,  or  an  artificial  myopia 
of  this  amount,  which  would  be  represented  by  a  far  point  of  13 
inches. 


What  proportionate  amount  of  ametropia  should  he  corrected  in 
a  person  20  year  of  age,  and  how  much  should  be  corrected  in  a  person 
50  years  of  age? 

In  a  person  20  years  of  age  we  might  correct  one-half  to 
two-thirds  of  the  ametropia,  or  perhaps  it  would  be  safer  to  say, 
the  manifest  defect.  In  a  person  50  years  where  the  accommoda- 
tion for  distance  need  scarcely  be  reckoned  with,  the  full  correction 
may  be  given. 

If  an  addition  to  a  prescription  for  distance  glasses  must  he 
made  for  preshyopia  of  -\-  3.50  D.  or  more,  ivhat  error  in  the  pre- 
scription for  distance  should  he  estimated? 

If  the  distance  glasses  were  convex  we  would  suspect  that 
the  hypermetropia  had  not  been  fully  corrected,  because  the 
presbyopic  addition  is  scarcely  ever  more  than  3  D. 


What  is  the  Maddox  rod,  and  for  ivhat  is  it  used? 

It  is  a  strong  cylinder  of  glass,  either  white  or  red,  which 
elongates  a  point  of  light  into  a  long,  narrow  streak  of  light  at 
right  angles  to  its  axis,  and  is  used  in  the  detection  of  the  various 
forms  of  heterophoria. 


Can  the  subjective  test  he  made  at  less  than  20  feet;  that  is 
where  20  feet  is  not  available? 

Yes,  if  allowance  is  made  for  the  increased  divergence  of  the 
rays  from  the  shorter  distances.  For  instance,  if  the  test  is  made 
at  a  distance  of  10  feet  the  rays  would  have  a  divergence  of  120 
inches,  which  is  equal  to  .^^  D.,  which  must  be  subtracted  from 
the  convex  correction  and  added  to  the  concave. 


204  State  Board  Examinations 

Some  operators  prefer  to  use  a  mirror,  which  in  a  10-foot 
room  gi\es  the  effect  of  20  feet. 


Where  should  the  base  of  the  prism  he  placed  in  measuring 
powers  of  adduction,  abduction,  supraduction  and  infraduction? 

The  apex  of  the  prism  is  placed  over  the  muscle  to  be  tested ; 
hence  adduction  is  measured  by  prism  base  out,  abduction  base  in, 
supraduction  base  down,  and  infraduction  base  up. 


Which  test  do  you  think  the  most  accurate  for  muscle  imbalance? 

There  may  be  some  difference  of  opinion  on  this  point,  but 
for  all  practical  purposes  we  should  say  the  Maddox  rod  test. 


In  cases  of  anisometropia  what  is  the  greatest  amount  of  dif- 
ference in  lenses  which  can  usually  be  worn  for  comfortable  binocular 
vision,  and  why? 

This  is  an  open  question,  as  the  difference  varies  in  each  case. 
Some  authorities  would  fix  the  limit  at  2  D.,  but  we  have  knowl- 
edge of  cases  where  the  difference  was  as  great  as  5  D.  This  is  a 
point  that  cannot  be  determined  by  any  rule,  but  only  by  actual 
trial. 

Is  the  test  with  the  perimeter  subjective  or  objective,  and  why? 

This  is  a  subjective  test,  because  the  information  to  be 
gained  is  dependent  upon  the  answers  of  the  patient. 


A  myope  of  5  D.  has  an  amplitude  of  accommodation  of  2  D. 
What  lenses  would  you  prescribe  for  reading  music  at  50  cm.  so  as 
to  permit  the  use  of  one-quarter  of  his  power  of  accommodation? 

The  full  amplitude  of  accommodation  is  2  D.,  but  he  is  to 
be  permitted  to  use  only  .50  D.  In  order  to  see  at  50  cm.  without 
any  accommodation  a-|-  2  D.  lens  is  required,  but  as  this  patient 
is  allowed  to  use  .50  D.  of  his  accommodation  then  only  +  1.50 
D.  is  necessary,  which  added  to  his  distance  glasses  would  reduce 
them  to  -  3.50  D. 


Practical  Optometry  205 

How  should  presbyope  be  tested  for  muscle  balance  at  fourteen 
inches? 

The  usual  method  is  by  means  of  the  dot  and  line  test  and  a 
vertical  prism.  Of  course,  the  necessary  convex  lenses  must  be 
worn  and  care  be  taken  to  see  that  they  are  properly  centered  for 
the  fourteen-inch  distance,  as  otherwise  the  lenses  themselves  will 
introduce  a  prismatic  effect. 

The  Maddox  rod  may  also  be  used  with  a  small  point  of  light 
at  the  indicated  distance  of  fourteen  inches. 


Under  what  conditions  would  you  consider  it  unwise  to  advise 
the  use  of  distance  glasses,  even  though  ametropia  were  present? 

If  any  disease  of  the  eye  calling  for  the  attention  of  a  medical 
man  was  known  to  be  present,  or  even  strongly  suspected,  it 
would  not  be  wise  for  an  optometrist  to  prescribe  glasses,  even 
though  an  error  of  refraction  was  also  discovered. 


Write  a  hypothetic  prescription  involving  prisms,  spheric  and 
cylindric  lenses. 

+  1.50  D.  sph.  C  +  .50  D.  cyl.  axis  90°  C  prism  2°  base  in. 


A  -{-  4  D.  sphere  is  placed  before  an  eye  that  is  2  D.  hyperme- 
tropic, and  an  object  twenty  inches  away  is  looked  at.  What  will 
be  the  character  of  the  image  on  the  retina? 

In  order  to  see  an  object  at  a  distance  of  20  inches  the 
emmetrope  will  use  2  D.  of  accommodation;  the  hypermetrope, 
in  addition,  must  use  sufificient  accommodation  to  overcome  his 
error;  therefore,  in  the  case  mentioned,  4  D.  of  accommodation 
will  be  required  at  20  inches.  If  now  a  +  4  D.  lens  is  placed 
before  the  eye  the  result  will  be  a  distinct  image  upon  the  retina 
without  effort  of  accommodation. 


'         When  the  targets  of  an  ophthalmometer  overlap  at  an  angle  of 
120°  and  separate  at  30°,  what  will  be  the  axis  of  the  concave  cylinder? 

This  would  indicate  that  the  greatest  refraction  was  located 
in  the  120th  meridian  and  the  least  in  the  30th  meridian;  there- 
fore, the  axis  of  a  concave  cylinder  would  coincide  with  the  latter. 


206  State  Board  Examinations 

Upon  what  general  principles  are  the  various  tests  for  muscle 
imbalance  based,  and  what  is  a  main  objection  to  these  tests? 

There  are  two  general  principles  on  which  the  various 
muscle  tests  are  based : 

1.  Those  which  displace  the  image  in  one  or  both  eyes  from 
the  macula  and  thus  produce  an  artificial  diplopia. 

2.  Those  in  which  the  image  formed  in  one  eye  is  changed 
in  color,  size  or  shape,  which  dissimilarity  in  the  two  retinal 
images  causes  diplopia. 

In  both  instances  binocular  vision  is  destroyed,  and  a  weak- 
ness in  any  of  the  muscles  is  supposed  to  manifest  itself. 

The  objection  to  the  first  class  of  tests  is  the  displacement 
from  the  macula,  but  in  both  of  them  we  have  no  means  of  know- 
ing how  much  innervation  is  sent  to  the  several  muscles  and  how 
much  of  the  heterophoria  may  thus  be  made  latent. 


//  a  presbyope  wearing  a  convex  lens  moves  it  farther  from  his 
eye  what  is  the  change  in  dioptric  power? 

The  effect  of  moving  a  convex  lens  farther  from  the  eye  is 
to  increase  its  dioptric  power. 


If  a  -\-  .50  D.  sphere  gives  best  vision  on  the  horizontal  lines 
of  the  astigmatic  fan,  and  a  -\-  1  D.  sphere  best  vision  on  the  vertical 
lines,  what  is  the  prescription  for  the  correcting  lens  written  in 
three  different  ways? 

+  .50  cyl.  axis  180°  C  +1  cyl.  axis  90° 
+  .50  D.  sph.  C  +  .50  D.  cyl.  axis  90° 
+  1  D.  sph.  C   -  .50  D.  cyl.  axis  180° 


In  trying  minus  lenses  on  a  myope  what  principal  rule  would 
you  constantly  keep  in  mind?  What  rule  in  cases  of  hypermetropia, 
using  plus  lenses? 

In  myopia  the  weakest  concave,  to  impose  as  little  tax  upon 
the  accommodation  as  possible. 

In  hypermetropia  the  strongest  convex,  to  assist  the  accom- 
modation as  much  as  possible. 


Practical  Optometry  207 

The  distance  test  shows  that  a  certain  patient  is  1.25  D.  hyper- 
metropic, hut  the  dynamic  test  with  the  cross  cylinder  at  20  inches 
shows  that  a  +  .25  sphere  cause  neutrality.  What  glasses  would 
you  prescribe? 

Not  stronger  than  +  -25  D.,  at  least  to  start  with. 


What  are  ''cover''  tests  and  what  is  their  object? 

A  screen  or  card  is  placed  before  one  eye,  which  is  watched 
to  discover  if  it  makes  any  movement  when  thus  covered.  If 
not  orthophoria  is  indicated.  If  it  moves  outward  there  is  a 
presumption  of  esophoria;  if  it  moves  inward  a  presumption  of 
exophoria. 

On  what  principle  does  the  Maddox  rod  test  act? 

That  it  causes  a  retinal  image  so  dissimilar  in  size,  shape 
and  appearance  from  the  other  that  the  natural  instinct  to  fuse 
them  into  one  is  for  the  time  being  destroyed,  and  in  this  way  a 
deficiency  in  any  of  the  muscles  becomes  manifest. 


Under  what  circumstances  wotdd  you  recommend  the  constant 
wearing  of  glasses? 

When  distant  vision  is  impaired,  when  headache  and 
symptoms  of  asthenopia  are  present,  in  high  errors  of  refraction 
and  usually  in  all  cases  of  astigmatism. 


What  acuity  of  vision  ivoidd  you  expect  to  find  in  a  young 
case  of  mixed  astigmatism,  in  which  the  corrected  cylinder  would  be 
50  D.  or  less,  with  the  rule?    Against  the  ride? 

In  a  case  of  mixed  astigmatism  the  accommodation  is  apt 
to  be  brought  into  play  to  overcome  the  hypermetropic  meridian, 
and  in  so  doing  it  makes  the  myopic  meridian  more  myopic. 
When  the  astigmatism  is  with  the  rule  it  is  the  vertical  meridian 
that  is  myopic,  which  is  the  meridian  that  focuses  horizontal 


208  State  Board  Examinations 

lines.  But  as  the  visibility  of  letters  largely  depends  upon  their 
vertical  lines,  under  these  circumstances  vision  would  be  little 
if  any  impaired. 

In  astigmatism  against  the  rule  the  horizontal  meridian  is 
the  myopic  one,  and  as  this  is  the  meridian  that  focuses  the 
vertical  lines  vision  is  more  likely  to  be  impaired. 


Under  ivhat  circumstances  should  hypermetropes  he  given  full 
correction? 

When  patient  is  past  middle  age,  distant  vision  impaired 
and  the  hypermetropia  practically  all  manifest. 

When  a  high  degree  of  esophoria  or  convergent  strabismus 
is  associated  with  the  refractive  error. 

When  a  partial  correction  fails  to  afford  relief. 


What  is  the  effect  on  the  ciliary  muscles  of  giving  a  full  correc- 
tion in  the  case  of  hypermetropes? 

The  ciliary  muscles  are  relieved  of  all  effort  in  distant  vision, 
and  are  called  into  use  only  for  the  accommodation  necessary 
in  near  vision,  just  as  is  the  case  in  emmetropia. 


Where  is  the  base  of  the  prism  placed  when  the  eye  turns  in? 
That  is,  for  constant  wear.  And  where  placed  to  exercise  the 
muscles? 

Base  out  for  constant  wear  and  base  in  for  exercise. 


How  can  we  with  a  stenopaic  disk  find  an  error  of  a  vertical 
meridian  in  a  case  of  astigmatism  which  requires  for  correction 
a  +  50  D.  cylinder  axis  180°? 

The  stenopaic  disk  is  placed  over  the  vertical  meridian  of 
the  eye  and  the  amount  of  hypermetropia  in  this  meridian 
measured  by  the  acceptance  of  convex  lenses,  or,  better  still, 
by  the  fogging  method. 

In  a  muscle  test  with  a  single  prism  over  the  right  eye  base 
down  the  upper  image  is  seen  on  the  left.  What  is  the  nature  of  the 
heterophoria  and  how  can  it  be  measured? 


Practical  Optometry  209 

The  upper  image  is  that  of  the  right  eye,  and  being  seen  on 
the  left  eye  indicates  exophoria.  It  can  be  measured  by  strength 
of  prism  base  in  that  it  brings  the  two  Hghts  in  the  same  vertical 
plane. 

How  can  the  near  point  of  convergence  he  found  objectively? 
Subjectively? 

By  the  near  point  of  convergence  is  understood  the  closest 
point  for  which  the  eyes  can  converge.  In  order  to  measure  it  a 
small  fixation  object  is  held  in  front  of  the  eyes  and  gradually 
brought  closer  and  closer. 

In  the  objective  test  the  eyes  are  sharply  watched,  and  as 
soon  as  one  of  them  ceases  to  converge  or  commences  to  diverge 
the  near  point  of  convergence  has  been  reached. 

In  the  subjective  test  the  object  is  approached  until  it  is 
seen  double  by  the  patient. 


A  myope  of  4  D.  has  an  amplitude  of  accommodation  of  3  D. 
He  is  to  befitted  with  glasses  to  read  at  16  inches,  hut  must  use  one- 
half  of  his  accommodation.     What  must  he  the  power  of  his  glasses? 

The  positive  refractive  power  of  such  an  eye  would  be  equal 
to  the  sum  of  the  amplitude  of  accommodation  and  the  myopia, 
or  7  D.  In  order  to  read  at  16  inches  2.50  D.  of  accommodation 
is  necessary,  but  if  he  must  use  only  one-hklf  of  his  accom- 
modation then  he  should  possess  5  D.  In  order  to  bring  about 
this  result  the  power  of  the  glass  required  would  be  —  2  D., 
which  reduces  the  7  D.  of  accommodation  to  the  desired  amount. 


When  plus  lenses  are  decentered  in,  what  extrinsic  muscles  are 
assumed  to  he  at  fault? 

The   effect   produced   being   that  of   prisms   bases   in,    the 
internal  recti  would  be  assumed  to  be  weak. 


A  patient  giving  his  age  as  thirty-five  years  requires  +  .50  D. 
for  distance  and  -{-2D.  for  reading.     What  would  you  suspect? 


2 1 0  State  Board  Examinations 

Would  suspect  that  the  +  .50  D.  did  not  represent  the  full 
correction  for  distance,  but  that  the  amount  of  hypermetropia 
was  more  nearly  equal  to  2  D.  and  that  the  proper  tests  had 
not  been  made  to  uncover  the  latent  error. 


In  two  given  cases,  each  patient's  age  being  thirty  years,  neither 
having  worn  glasses  before,  normal  vision  is  obtained  with  spherical 
correction.  One  is  hypermetropic  2  D.  and  has  2°  of  exophoria; 
the  other  is  myopic  2  D.  and  has  2°  of  esophoria.  Write  prescrip- 
tions for  both. 

When  hypermetropia  occurs  in  connection  with  exophoria, 
and  myopia  in  connection  with  esophoria,  there  is  a  disturbance 
of  the  normal  relation  that  should  exist  between  the  accommoda- 
tion and  the  convergence. 

In  the  first  case  we  would  be  inclined  to  undercorrect 
the  hypermetropia  because  convex  lenses  tend  to  aggravate 
exophoria;  or  we  would  combine  a  prism  base  in  to  correct  the 
exophoria,  not  exceeding  one-half  the  amount  of  insufficiency. 

In  the  second  case  we  would  also  think  of  undercorrection, 
because  a  concave  lens  tends  to  increase  an  esophoria ;  or  we  would 
combine  a  prism  base  out  with  the  concave  lens,  not  attempting 
to  correct  more  than  one-half  the  heterophoria. 


What  course  should  be  followed  in  prescribing  for  anisometropes 
whose  eyes  differ  widely  in  refraction? 

Correct  the  best  eye  fully  and  the  other  eye  approximately. 
In  other  words,  take  care  of  the  good  eye  and  do  what  you  can 
for  the  poorer  eye  at  the  time,  with  the  thought  of  gradually 
increasing  the  correction  of  the  latter,  as  the  comfort  of  the 
eyes  will  allow.  The  visual  acuity  of  each  eye,  as  well  as  the 
muscle  balance,  must  be  taken  into  account.  It  is  impossible 
to  give  general  directions  that  will  apply  to  all  cases,  but  each 
case  must  be  managed  on  its  own  merits. 


.     Give  reasons  why  it  is  sometimes  not  advisable  to  prescribe 
distance  glasses. 


Practical  Optometry  211 

When  the  acuteness  of  vision  is  not  impaired,  when  the 
refractive  error  is  small,  when  there  is  no  headache  or  photo- 
phobia or  evidence  of  eyestrain  in  general  vision,  and  when 
glasses  cause  so  much  fogging  of  distant  vision  as  to  be  unbear- 
able. 

Under  what  conditions  should  the  constant  wearing  of  glasses 
he  insisted  on? 

In  case  of  strabismus  due  to  refractive  error,  in  almost  all 
cases  of  astigmatism,  when  headache  is  present  due  to  eyestrain, 
and  when  vision  is  very  greatly  improved  by  the  glasses. 


Under  what  circumstances  might  a  concave  lens  be  prescribed 
for  a  hypermetrope? 

The  optical  student  is  so  much  cautioned  about  the  danger 
of  giving  concave  lenses  to  a  hypermetrope  that  when  he  gets 
into  practice  he  would  not  want  to  be  accused  of  such  ignorance 
as  this  question  would  seemingly  display.  And  while  this 
teaching  is  correct,  there  are  cases  of  hypermetropia  with  in- 
sufficient convergence,  in  which  it  might  be  allowable  to  prescribe 
concave  lenses  for  temporary  use  for  their  indirect  effect  of 
stimulating  the  convergence. 


Give  reasons  for  and  against  full  correction  of  myopia  and 
hypermetropia  in  (a)  orthophoria  and  (b)  heterophoria. 

(a)  In  orthophoria,  w^e  give  the  strongest  convex  lens  in 
hypermetropia  and  the  weakest  concave  lens  in  myopia,  in  order 
to  assist  the  accommodation  or  lessen  the  strain  upon  it. 

(6)  In  heterophoria,  the  above  rule  must  be  modified  in 
the  light  of  the  effect  of  the  lenses  upon  the  accommodation  and 
convergence. 

When  hypermetropia  has  esophoria  associated  with  it,  the 
full  correction  is  given;  but  when  exophoria  is  present,  it  is  best 
to  under-correct,  because  convex  lenses  aggraN'ate  exophoria. 

In  the  case  of  myopia  with  exophoria,  the  full  correction 
may  be  given;  but  when  esophoria  is  present,  the  concave  lenses 


212  State  Board  Examinations 

should   not   be   too   strong,   because   concave   lenses   aggravate 
esophoria. 

What  is  the  usual  method  of  employing  the  stenopaic  slit  in 
testing  the  eye,  and  why  is  it  not  in  common  use? 

While  the  patient  looks  at  the  card  of  test  letters  the  slit 
is  rotated  to  the  meridian  of  best  vision,  in  which  position  trial 
lenses  are  used  to  determine  if  this  meridian  is  emmetropic, 
hypermetropic  or  myopic.  The  slit  is  then  rotated  to  the  meridian 
at  right  angles  where  test  lenses  are  used  to  determine  if  it  is 
hypermetropic  or  myopic.  Having  estimated  in  this  way  the 
refractive  condition  of  the  two  principal  meridians,  it  is  easy 
to  formulate  the  cylinder  or  sphero-cylinder  that  is  required  to 
correct. 

It  is  scarcely  reliable  because  the  accommodation  is  likely 
to  come  into  play  and  may  be  used  more  in  one  meridian  than 
the  other,  thus  impairing  the  accuracy  of  the  test. 


When  may  myopes  be  given  the  strongest  possible  lenses  to 
produce  normal  vision? 

The  standard  advice  to  prescribe  the  weakest  concave 
lenses  in  myopia  may  be  modified  in  young  people  when  exo- 
phoria  is  present. 

Of  two  equally  far  sighted  persons,  one  has  the  habit  of  ivearing 
his  spectacles  low  down  on  his  nose,  the  other  wears  them  close  to 
his  eyes.  Which  should  have  the  stronger  spectacles,  the  object 
being  held  at  the  same  distance  from  the  eye  by  both  persons?  Give 
the  reason  for  your  answer? 

It  is  a  well-known  fact  that  convex  lenses  increase  in  power 
as  they  are  pushed  farther  from  the  eye.  In  these  cases  we  are 
led  to  infer  that  they  are  both  under-corrected.  In  the  first 
case  the  person  has  learned  that  he  can  get  the  extra  power  that 
is  needed  by  wearing  his  spectacles  low  down  on  his  nose. 

The  second  person  either  has  not  learned  this  trick  or  he 
prefers  to  wear  his  glasses  in  their  proper  place  close  up  to  the 
eyes,  and  therefore  he  is  the  one  that  should  have  stronger 
spectacles. 


Practical  Optometry  213 

A  patient  with  a  pupillary  distance  of  59  mm.  wears  -\-  4  D. 
lenses  for  distance  in  a  spectacle  frame  with  a  pupillary  width  of 
61  mm.    What  is  the  effect  of  the  lens  and  what  is  the  amount? 

Under  these  conditions  patient  would  not  look  through 
optical  centers  of  lenses  and  therefore  a  prismatic  effect  would 
be  produced;  and  as  the  spectacle  frames  are  too  wide  for  the 
pupillary  distance  of  the  patient,  and  as  the  lenses  are  convex, 
the  prismatic  effect  would  be  bases  out. 

Figuring  on  the  basis  of  1°  of  prism  for  every  1  D.  decentered 
10  mm.,  and  as  the  amount  of  decentration  in  this  case  is  2  mm., 
the  amount  of  prismatic  power  developed  would  be  4/5°  for  each 
lens. 

Patient  aged  forty-five  has  worn  -}-  1  D.  cyl.  axis  180°  with 
comfort  for  years  previously,  but  now  complains  that  reading 
in  evenings  is  uncomfortable.  What  would  be  your  treatment  of  the 
case? 

This  patient  has  now  reached  the  presbyopic  period  of 
life,  and  the  cylinders  worn  for  the  correction  of  his  refractive 
error  will  no  longer  suffice  for  close  use,  but  must  be  supplemented 
by  the  addition  of  convex  spheres  for  the  correction  of  the 
presbyopia,  which  at  this  age  would  probably  be  about  +  1  D. 

I  would  re-examine  his  eyes  and  ascertain  just  what  is 
needed  for  distance  and  for  reading,  and  give  him  the  choice 
between  bifocals  and  two  pairs  of  glasses.  If  separate  pairs  of 
glasses  are  ordered  for  close  use,  it  is  more  than  probable  the 
cylinders  may  be  reduced  somewhat,  as  is  usually  the  case  with 
convex  cylinders  having  a  horizontal  axis,  because  of  the  fact 
that  when  looking  down  through  convex  lenses,  as  in  reading, 
there  is  produced  the  added  effect  of  a  cylinder  with  a  horizontal 
axis,  thus  allowing  the  cylindrical  surface  of  the  lens  to  be  reduced 
somewhat. 

In  the  case  of  astigmatic  presbyopes  is  it  always  necessary  to 
retain  the  cylinder  in  the  reading  glasses?  And  what  is  the  cause 
of  the  difficulty  experienced  by  presbyopes  in  getting  accustomed  to 
wearing  cylinders? 

As  a  rule,  if  the  astigmatism  is  of  such  a  character  as  to 
cause  symptoms  of  discomfort,  it  will  be  corrected  earlier  in  life, 


214  State  Board  Examinations 

and  then  w  hen  the  patient  reaches  the  presbyopic  age,  it  simply 
means  the  addition  of  a  convex  sphere  of  such  power  as  will 
afTord  comfortable  reading  at  the  proper  distance. 

But  it  sometimes  happens  that  persons  who  have  passed 
their  fortieth  year  will  apply  for  glasses,  with  the  history  that 
they  have  never  worn  them,  or  felt  the  need  of  them,  but  of  late 
they  are  beginning  to  experience  some  difficulty  in  close  vision. 

The  optometrist  starts  to  make  his  examination  in  the  usual 
way  and  soon  finds  the  existence  of  astigmatism,  perhaps  .50  D. 
to  1  D.  He  remembers  that  he  was  taught  that  astigmatism  is  a 
frequent  cause  of  eyestrain  and  headache,  and  if  he  has  not  had 
much  practical  experience  he  will  proceed  to  correct  it  and 
perhaps  get  himself  into  trouble,  because  the  patient  returns 
and  complains  that  the  glasses  are  uncomfortable. 

Another  examination  will  show  the  presence  of  the  same 
amount  of  astigmatism  as  at  the  first,  and  perhaps  the  patient 
will  be  advised  to  persevere  with  the  sphero-cylinders,  but  with 
probably  the  same  result  as  before. 

This  brings  up  the  question  as  to  why  it  is  more  difficult  for 
older  persons  to  become  accustomed  to  cylinders  than  younger 
ones.  Now,  it  must  be  borne  in  mind  that  vision  is  not  so  much 
a  question  of  physical  optics  as  of  physiological  optics,  and  that 
there  is  a  psychological  feature  as  w^ell;  in  other  words,  there  is 
not  only  the  formation  of  an  image  on  the  retina,  but  also  the 
interpretation  of  that  image  by  the  brain.  It  is  not  the  eye 
that  sees  but  really  the  brain. 

Astigmatism  causes  some  distortion  in  the  retinal  image, 
but  it  is  not  noticeable  to  the  patient,  because  it  has  always 
existed,  and,  in  fact,  the  sense  of  vision  was  acquired  and  culti- 
vated with  that  kind  of  an  image.  For  instance,  a  square  object 
would  not  form  a  perfectly  square  image  in  an  astigmatic  eye, 
but  would  be  elongated  in  one  direction  or  the  other,  according 
to  the  character  of  the  error. 

The  person,  how^ever,  knows  by  education  and  experience 
that  the  object  is  actually  square  and  his  brain  learns  to  interpret 
the  slightly  distorted  retinal  image  as  that  of  a  square  object, 
and  he  is  satisfied  with  his  vision. 

When  the  proper  correcting  cylinders  are  placed  before  the 
eye,  the  image  of  a  square  object  is  also  square;  but  it  is  different 
from  what  the  brain  has  been  accustomed   to  recognize  as  a 


Practical  Optometry  215 

square  object,  and  hence,  even  though  the  image  is  square,  the 
object  appears  to  be  elongated. 

The  greater  number  of  the  cyHnders  that  are  worn  are 
prescribed  more  for  the  relief  of  asthenopia  than  for  the  improve- 
ment in  vision;  but  even  in  the  higher  degrees  of  astigmatism 
where  the  acuteness  of  vision  is  much  less  than  normal,  the 
correcting  cylinders,  though  they  afford  perfect  vision,  are 
oftentimes  disappointing  and  unsatisfactory  for  the  reasons 
mentioned  above.  The  patient  is  expecting  great  things  and 
when  he  finds  that  the  results  are  not  as  good  as  before,  he  is 
apt  to  become  disgusted. 

A  myope  of  6  D.  possessing  3  D.  of  accommodation,  wants  a 
pair  of  glasses  for  reading  at  16  inches.  If  it  is  desired  that  only 
one-half  the  power  of  accommodation  be  used,  what  would  be  the 
strength  of  the  glasses  you  would  give? 

In  determining  the  reading  glasses  in  high  myopia,  the  rule 
is  as  follows :  Subtract  the  glass  representing  the  desired  reading 
point  from  the  full  measure  of  the  myopia.  In  this  case  the  glass 
representing  the  desired  reading  point  of  16  inches  is  2.50  D., 
which  we  subtract  from  the  full  amount  of  myopia  which  is  6  D., 
and  the  result  is  —  3.50  D. 

With  these  —  3.50  D.  glasses  there  remains  an  uncorrected 
myopia  of  2.50  D.,  which  represents  a  far  point  of  16  inches,  at 
which  distance  the  person  would  be  able  to  read  without  any 
effort  of  accommodation. 

But  we  are  told  it  is  desired  to  use  one-half  of  his  3  D.  of 
accommodation  and,  therefore,  to  bring  this  amount  of  accom- 
modation into  action,  a  —  1.50  D.  lens  must  be  added  to  the 
—  3.50  D.  lens,  which  means  that  the  glasses  to  be  prescribed  to 
accomplish  the  purpose  indicated  must  be  —  5  D. 


Can  a  concave  lens  have  conjugate  foci?  If  so,  under  what 
conditions? 

When  parallel  rays  of  light  enter  a  concave  lens,  they  are 
made  divergent  to  such  an  extent  as  to  appear  to  come  from 
the  principal  focal  distance  of  the  lens.  If  the  power  of  the  lens 
is  —  4  D.,  the  rays  after  refraction  will  apparently  diverge  from 
a  point  10  inches  in  front  of  the  lens. 


216  State  Board  Examinations 

But  when  the  rays  proceed  from  an  object  nearer  than 
infinity,  in  other  words  when  the  rays  that  enter  the  lens  are 
already  divergent,  they  are  made  still  more  divergent  by  the 
action  of  the  lens.  The  divergence  produced  by  the  lens  is 
increased  by  the  divergence  caused  by  the  nearness  of  the  object, 
and,  therefore,  the  rays  will  appear  to  diverge  from  a  point 
closer  than  the  principal  focus,  which  point  would  be  conjugate 
to  the  object. 


Fig.  32 


In  this  diagram  it  will  be  seen  that  the  rays  diverging  from 
fi,  which  is  the  location  of  the  object,  will  be  still  more  diverged 
by  the  action  of  the  lens  so  as  to  appear  to  proceed  from  fo, 
which  is  assumed  to  be  the  location  of  the  negative  focus  and  is 
conjugate  to  fi. 

Suppose  in  the  above  diagram  the  lens  is  an  8-inch  concave, 
and  the  distance  of  fi  is  40  inches;  then  the  rays  enter  the  lens 
with  a  divergence  of  1/40,  to  which  is  added  the  divergent  power  of 
the  lens,  which  is  1/8,  and  the  rays  after  refraction  will  have  a 
divergence 

4J     +      8      ~      4J     "    6% 
U  is  negative  and  6  2/3  inches  in  front  of  the  lens. 

If  rays  diverge  from  40  inches  to  an  8-inch  concave  lens, 
they  are  after  refraction  divergent  as  if  from  6  2/3  inches. 


//  a  patient  comes  to  you  wearing  -{-ID.  spheres  for  distance 
and  -\-  6  D.  spheres  for  reading,  woidd  this  seem  right  to  you? 
If  iiot,  point  out  where  the  error  is  likely  to  lie. 

We  must  assume  that  this  is  a  case  of  hypermetropia  with 
presbyopia,  and  as  such  the  history  would  be  more  complete  if 
we  knew  the  age  of  the  patient.     However,  we  will  consider  the 


Practical  Optometry  217 

presbyopia  as  complete,  or  in  other  words  that  the  ampHtude  of 
accommodation  has  been  entirely  lost. 

Under  such  circumstances  the  focal  distance  of  the  lens 
required  for  reading  should  correspond  to  the  desired  reading 
distance,  as,  for  example,  with  entire  suspension  of  accommoda- 
tion a  +  2.50  D.  lens  would  afford  a  reading  distance  of  16 
inches,  a  +  3  D.  lens,  a  reading  distance  of  13  inches,  and  so  on. 

The  latter  has  come  to  be  regarded  as  a  proper  reading 
distance,  and  therefore,  the  strength  of  the  lens  required  even 
in  total  presbyopia  is  seldom  more  than  3  D.  or  perhaps  +  3.50  D. 

When  we  come  to  consider  this  case  we  see  that  there  is  an 
addition  of  5  D.  apparently  to  correct  the  presbyopia,  which, 
in  view  of  the  above,  is  too  much.  Now,  then,  it  is  probable 
that  the  +  6  D.  lenses  are  necessary  to  afford  clear  vision  at 
the  customary  reading  distance,  and  therefore  we  would  infer 
that  instead  of  the  reading  glasses  being  too  strong,  the  distance 
glasses  are  too  weak. 

This  error  is  probably  due  to  the  carelessness  of  the  optom- 
etrist who  made  the  examination.  He,  perhaps,  placed  the 
-f-  1  D.  lenses  before  the  patient's  eyes,  which  caused  a  marked 
improvement  in  distant  vision  and  which  the  patient  may  have 
declared  splendid.  And  on  such  declaration  the  glasses  were 
prescribed,  instead  of  following  the  rule  to  find  the  strongest 
lenses  that  afforded  good  distant  vision. 

We  think  a  further  examination  of  such  a  case  would  show 
that  the  hypermetropia  was  probably  equal  to  3  D.  with  an 
addition  of  a  similar  amount  needed  for  reading. 


Pathological  Optometry 

Defiite  paresis  and  paralysis.  Tell  hotv  you  would  diagnose 
each  condition. 

The  words  paresis  and  paralysis  are  often  used  inter- 
changeably, but  usually  the  former  is  understood  to  apply  to 
milder  cases.  Paralysis  is  applied  to  that  condition  where  there 
is  a  loss  of  power  of  motion  or  sensation,  and  paresis  to  that 
condition  in  which  there  is  a  slight  form  of  paralysis. 

If  there  is  paralysis  in  the  internal  rectus  there  would  be  a 
total  loss  of  the  power  to  turn  the  eye  inwards.  The  eyes  may 
assume  a  position  of  parallelism,  but  there  is  more  likely  to  be 
a  slight  divergence,  which  would  result  in  crossed  diplopia,  which 
is  increased  by  trying  to  converge  or  look  inwards,  and  diminishes 
or  disappears  when  looking  outwards  or  away  from  affected 
muscle. 

In  paresis  the  limitation  of  movement  would  be  less  notice- 
able and  the  strabismus  and  diplopia  would  be  less  observable, 
perhaps  only  detectable  when  extreme  convergence  is  attempted. 


What  is  the  difference  between  conjunctivitis  and  keratitis? 

The  first  is  an  inflammation  of  the  conjunctiva  and  the 
second  of  the  cornea. 

The  symptoms  of  conjunctivitis  are  congestion  of  the  ocular 
palpebral  conjunctiva,  a  burning  and  scratching  as  if  sand  was 
in  the  eye,  a  discharge — at  first  watery,  afterwards  muco- 
purulent; vision  but  slightly  impaired,  photophobia  not  very 
marked,  slight  swelling  of  the  lids. 

The  symptoms  of  keratitis  indicate  great  irritability. 
Marked  photophobia,  excessive  lachrymation  and  circumcorneal 
injection.  Vision  blurred  on  account  of  infiltration  of  the  layers 
of  the  cornea.  Blood  vessels  are  seen  in  the  cornea.  Pain  is 
considerable.  The  inflammation  may  extend  to  the  iris  (iritis) 
and  even  to  the  ciliary  body  and  choroid. 

218 


Pathological  Optometry  219 

Describe  hemorrhage  of  the  retina. 

Hemorrhage  may  occur  in  any  layer  of  the  retina  or  in  any 
portion  of  its  surface.  Its  color  is  at  first  bright  red,  later  it 
becomes  darker,  and  may  finally  be  entirely  absorbed. 

The  most  common  seat  of  retinal  hemorrhage  is  in  the  region 
of  the  disk  and  next  in  the  neighborhood  of  the  macula,  the 
latter  disturbing  vision  more  and  more  as  the  macula  is  ap- 
proached. Hemorrhages  occur  mostly  between  the  fibers  of  the 
inner  layer  and  present  a  flame-shape  appearance.  Those  which 
occur  in  the  outer  layers  are  more  apt  to  be  round  or  irregular 
in  shape. 

A  hemorrhage  may  sometimes  be  so  profuse  as  to  break 
through  the  hyaloid  membrane  and  escape  into  the  vitreous. 

The  causes  of  retinal  hemorrhage  are  degeneration  of  the 
walls  of  the  blood  vessels  as  found  in  advanced  life,  heart  disease, 
sudden  reduction  of  tension,  as  after  the  operation  for  glaucoma, 
pernicious  anaemia,  gout,  etc. 


What  is  complete  dislocation  of  the  lens  called? 

In  complete  dislocation  of  the  lens  the  optical  condition  is 
one  of  aphakia;  that  is,  high  hypermetropia  and  entire  loss  of 
accommodation. 

Name  a  disease  of  the  eyes  on  account  of  which  immigrants 
are  refused  admission  to  this  country.    Give  reason. 

Trachoma,  because  of  its  contagiousness,  due  to  the  presence 
of  a  micro-organism  in  the  discharge.  It  has  a  tendency  to  spread 
in  certain  countries,  among  certain  races  and  in  crowded  institu- 
tions. Bad  air,  overcrowding,  poor  food  and  filth  contribute  to 
its  de\'elopment  in  connection  w^ith  the  contagion. 


What  is  pterygium? 

Pterygium  is  a  vascular  thickening  of  the  conjunctiva, 
triangular  in  shape,  on  the  nasal  side  of  the  cornea,  with  the 
apex  of  the  growth  towards  the  latter.  Sight  is  not  impaired 
unless  the  pterygium  extends  over  the  pupillary  region  of  the 
cornea.    The  treatment,  if  any  is  required,  is  surgical. 


220  State  Board  Examinations 

What  is  color  blindness? 

Complete  color  blindness  would  mean  an  entire  absence  of 
the  color  sense  in  which  case  a  landscape  would  look  like  an 
engraving — a  picture  entirely  colorless.  This,  however,  is  very 
rare. 

Partial  color-blindness,  as  it  is  usually  encountered,  is  due 
to  a  loss  of  sensation  for  one  of  the  three  fundamental  colors, 
red,  green  and  violet.  Red  color-blindness  is  the  most  common. 
This  defect  is  found  most  frequently  in  men  and  is  doubtless  to 
some  extent  a  matter  of  education. 


What  is  conical  cornea? 

A  diseased  condition  in  which  the  cornea  is  altered  in 
shape  and  bulges  forward  in  the  form  of  a  cone.  This  is  due  to 
a  gradual  atrophic  process  in  the  central  part  of  the  cornea,  as 
a  result  of  which  the  intraocular  tension  causes  it  to  bulge. 
The  transparency  of  the  cornea  is  not  much  impaired.  The 
condition  is  easy  of  diagnosis  because  it  is  evident  on  mere 
inspection. 


What  is  color  blindness  and  what  effect  does  it  have  on  visual 
acuity? 

Color  blindness  is  an  inability  to  distinguish  between  certain 
colors.  As  a  rule,  it  does  not  impair  the  visual  acuity,  nor  in- 
terfere with  reading,  writing  or  the  ordinary  occupations  of  life. 


Of  what  does  the  operation  for  cataract  consist? 

In  the  removal  from  the  eye  of  the  crystalline  lens,  which 
has  lost  its  transparency  and  become  opaque. 


What  causes  a  posterior  staphyloma? 

This  is  a  bulging  backward  of  the  eyeball  and  occurs  in 
high  myopia.  In  these  cases  there  is  usually  an  increased 
pupillary  distance,  which  in  connection  with  the  close  position 
at  which  work  is  done  imposes  an  unnatural  tax  upon  the  con- 


Pathological  Optometry  221 

vergence.  This  latter  pressure  from  tension  of  the  recti  muscles 
tends  to  an  elongation  of  the  ball,  which  is  facilitated  by  the 
softening  of  the  tissues  of  the  posterior  half  of  the  eye,  due  to 
the  accompanying  scleritis  and  choroiditis,  which  is  so  common 
in  myopia. 

What  is  aphakia? 

A  condition  of  the  eye  in  which  the  crystalline  lens  is  absent, 
either  naturally  or  artificially,  as  in  the  operation  for  cataract. 


What  is  glaucoma,  and  name  one  prominent  symptom? 

A  disease  which  seriously  threatens  vision  on  account  of 
abnormal  intraocular  tension,  and  its  one  prominent  symptom 
is  a  stony  hardness  of  the  eyeball. 


What  part  of  the  eye  is  affected  in  conjunctivitis? 
The  mucous  membrane  called  the  conjunctiva. 


What  part  of  the  eye  is  affected  in  iritis? 
The  iris. 

What  wotild  lead  you  to  believe  that  your  patient  was  suffering 
from  cataract? 

The  oncome  of  second  sight  would  at  once  lead  to  the  sus- 
picion of  cataract.  In  such  cases  there  is  a  condition  of  refractive 
myopia,  due  to  a  softening  and  swelling  and,  as  a  result,  an 
increase  in  power  of  the  crystalline  lens.  This  is  apt  to  occur 
in  the  60's,  and  such  a  person  who  has  been  depending  upon 
convex  lenses  for  reading  now  finds  he  is  able  to  read  without 
glasses.  This  is  almost  invariably  a  premonitory  symptom  of 
cataract. 

Also  if  smokiness  of  vision  and  spots  before  eyes  were  com- 
plained of  cataract  would  be  suspected.  In  advanced  stages  of 
the  disease  cataract  is  easily  detected  even  in  ordinary  daylight 
by  the  grayish  appearance  of  the  pupil.     In  the  earlier  stages 


222  State  Board  Examinations 

cataract  is  discovered  by  an  ophthalmoscopic  examination,  the 
opacities  showing  as  dark  spots  on  the  red  background. 


What  is  meant  by  the  expression  "woolly''  appearance  around 
the  edge  of  the  optic  nerve? 

This  term  is  used  to  express  the  appearance  of  the  disk  in 
papillitis  or  inflammation  of  the  optic  nerve  head,  in  which  the 
disk  is  swollen,  red  and  with  a  blurring  of  its  border  by  a  grayish 
opalescent  haze.  This  haziness  may  become  a  decided  opacity, 
covering  and  extending  beyond  the  border  of  the  disk,  and 
later  pass  into  a  condition  of  atrophy. 


A  person  cannot  see  distant  objects  clearly.  What  are  the 
possible  reasons? 

In  a  general  way  we  say  the  impairment  of  distant  vision 
may  be  due  either  to  refractive  error  or  disease. 

Any  error  of  refraction,  myopia,  hypermetropia  or  astigma- 
tism may  be  the  cause  of  it,  especially  myopia  and  high  degrees 
of  hypermetropia  and  astigmatism. 

In  regard  to  diseases  there  may  be  cataract  or  opacity  of 
any  of  the  refracting  media  and  affections  of  the  optic  nerve  and 
retina. 

What  is  the  cause  of  strabismus  in  young  children? 

During  the  first  few  months  of  life  the  movements  of  the 
eyes  are  uncertain  and  are  not  controlled  by  the  brain.  It  is 
not  until  the  end  of  the  first  year  that  binocular  vision  is  estab- 
lished. In  the  absence  of  the  natural  desire  for  binocular  vision 
there  is  no  incentive  for  accord  between  the  movements  of  the 
two  eyes,  under  which  circumstances  any  slight  cause  may  upset 
the  equilibrium  of  the  higher  centers  of  the  brain.  Hence  babies 
often  squint  from  gastric  or  other  disturbances. 

But  in  the  great  majority  of  young  children  where  the 
strabismus  is  of  the  convergent  concomitant  form  and  appears 
by  the  fourth  year,  it  is  due  to  hypermetropia,  which  is  the 
predominant  error  of  refraction  in  children  and  which  imposes 
an  extra  tax  on  the  accommodation,  and  thus  stimulates  the 
convergence. 


Pathological  Optometry  223 

What  is  mixed  astigmatism  and  what  kind  of  a  lens  is  required 
to  correct  it? 

That  condition  in  which  one  meridian  is  hypermetropic  and 
the  other  meridian  at  right  angles  is  myopic.  It  is  corrected  by 
a  cross-cylinder,  the  convex  element  of  which  corrects  the 
hypermetropic  astigmatism,  and  the  concave  element  the 
myopic  astigmatism.  The  axes  of  the  cylinders  are  at  right 
angles  to  each  other,  and  this  cross-cylinder  may  be  transposed 
to  a  sphero-cylinder. 

The  far  point  of  a  myope  is  at  10  cm.  and  his  near  point  is 
at  5  cm.     What  is  his  myopia  and  what  is  his  accommodation? 

His  myopia  as  estimated  by  his  far  point  is  10  D.  and  his 
amplitude  of  accommodation  as  shown  by  his  near  point  is  20  D. 


What  is  meant  by  the  terms  astigmatism  with  the  rule  and 
astigmatism  against  the  rule? 

Usually  the  normal  eye  shows  a  slight  excess  of  curvature  in 
the  vertical  meridian  of  the  cornea;  hence  in  any  case  of  astigma- 
tism where  the  vertical  meridian  exceeds  in  refractive  power  w^e 
term  it  "with  the  rule,"  and  w^here  the  horizontal  meridian  is 
in  excess,  "against  the  rule." 


What  kind  of  astigmatism  cannot  be  satisfactorily  corrected 
with  glasses,  and  why? 

Irregular  astigmatism,  because  in  these  cases  there  is  a 
difTerence  in  refraction  in  different  parts  of  the  same  meridian, 
and  it  is  obvious  that  glasses  could  not  be  ground  in  such  a  way 
as  to  correct  this  condition. 


What  kind  of  strabismus ,  if  any,  is  usual  with  pronounced 
hypermetropia? 

Convergent  concomitant  strabismus,  on  account  of  the  close 
relation  existing  between  accommodation  and  convergence.  In 
hypermetropia  where  the  accommodation  must  be  used  in 
excess  of  normal,  the  convergence  is  stimulated  into  excessive 
action  and  manifests  itself  by  a  turning  in  of  one  or  the  other  eye. 


224  State  Board  Examinations 

The  far  point  of  a  certain  eye  is  33  cm.  behind  the  eye,  and  the 
near  point  is  33  cm.  in  front  of  the  eye.  What  is  the  character  of 
the  refractive  error,  and  what  is  the  amplitude  of  accommodation? 

Hypermetropic  to  the  extent  of  3  D.  and  an  amplitude  of 
accommodation  of  6  D.  to  overcome  the  hypermetropia  and  show 
a  near  point  of  3i  cm. 

The  far  point  of  an  eye  is  1/3  of  a  meter  in  front  of  the  eye. 
What  is  the  kind  of  error,  and  what  lens  is  required  to  make  this  eye 
emmetropic? 

Myopia,  requiring  a  —  3  D.  to  make  it  emmetropic. 


An  eye  is  hypermetropic  2  D.  in  the  vertical  meridian  and  2.50 
D.  in  the  horizontal.  Write  four  different  prescriptions  of  glasses 
to  fully  correct  the  error  of  refraction. 

+  2  D.  cyl.  axis  180°  C  +  2.50  D.  cyl.  axis  90° 
+  2  D.  sph.  C  +  .50  D.  cyl.  axis  90° 
+  2.50  D.  sph.  C   -  .50  D.  cyl.  axis  180° 
Toric  +  6  D.  vertically  +  6.50  D.  horizontally  with  —  4  D. 
for  inner  surface. 


An  old  person  has  no  accomodation  left.  To  see  distinctly  at 
33  cm.  he  required  +  2.25  D.  sphere.  What  would  be  the  prescrip- 
tion for  distance  and  for  reading  music  at  80  cm.? 

In  order  to  see  distinctly  at  2)2>  cm.  without  eflfort  of  accom- 
modation a  +  3  D.  lens  would  ordinarily  be  required;  but  as  in 
this  case  it  was  possible  with  a  +  2.25  D.  lens,  we  must  assume 
that  the  other  .75  D.  is  supplied  by  the  eye,  which  could  be  done 
only  if  the  eye  was  myopic  to  that  extent. 

For  vision  at  80  cm.  without  accommodation  a  -\-  1.25  D. 
lens  would  be  called  for,  which  in  this  case,  where  the  refraction 
is  myopic,  .75  D.  would  be  reduced  to  +  .50  D. 

Therefore  the  prescriptions  would  be  as  follows : 

Distance  -  .75  D.;   at  80  cm.  +  .50  D. 


In  cases  of  myopia  when  may  this  condition  be  expected  to 
show  itself? 


Pathological  Optometry  225 

During  school  life,  when  the  eyes  are  taxed  to  the  utmost 
perhaps  with  insufficient  light  and  under  unfavorable  conditions, 
the  first  indication  being  a  tendency  to  hold  the  book  close  to  the 
eyes.  

What  is  the  far  point  of  an  eye  ivkich  needs  a  —  6  D.  to  make  it 
emmetropic? 

About  six  and  a  half  inches. 


What  is  the  difference  between  latent  strabismus  and  hetero- 
phoria? 

No  practical  difTerence,  as  both  terms  are  used  to  express  the 
same  condition.  

In  the  case  of  anisometropes  one  retinal  image  may  be  larger 
than  the  other,  and,  therefore,  the  two  eyes  cannot  act  together.  Hoiv 
can  we  settle  this  point? 

By  placing  before  each  eye  its  proper  correction  and  directing 
the  patient's  attention  to  a  single  line  of  letters  across  the  room. 
A  5°  prism  is  placed  vertically  before  one  eye  and  the  patient  will 
see  two  lines  of  letters,  one  under  the  other,  one  belonging  to  each 
eye.  The  patient  is  asked  which  is  the  plainer,  the  upper  or  the 
lower.  In  this  way  can  be  quickly  determined  which  eye  has  the 
best  vision  and  an  effort  made  to  improve  that  of  the  poorer  eye 
so  as  to  place  them  as  nearly  as  possible  on  an  equality. 

The  general  rule  in  anisometropia  is  to  take  care  of  the  good 
eye  and  give  it  its  proper  correction,  with  an  approximate  cor- 
rection to  the  other  eye  for  the  time  being,  which  can  later  be 
raised  more  and  more  to  full  correction. 


In  a  case  show-ing  by  the  trial  case  test  a  full  correction  with 
—  .50  spheres,  what  would  lead  you  to  suspect  that  there  was  a  spasm 
of  accommodation? 

Inasmuch  as  hypermetropia  is  the  predominant  error  of 
refraction,  and  as  its  detection  is  important  because  it  is  the  chief 
cause  of  eyestrain,  it  is  proper  to  suspect  this  error  in  all  cases 
until  pro\'ed  otherwise.  Slight  degrees  of  myopia  are  few,  and  as 
weak  concave  lenses  are  readily  accepted  b\'  all  young  people  such 
acceptance  should  at  once  raise  the  suspicion  of  spasm  of  accom- 


226  Slate  Board  Examinations 

modation,  and  then  the  fogging  system  must  be  patiently  and 
persistently  used. 

What  is  the  cause  oj  presbyopia  and  when  does  it  begin? 

Due  to  the  increasing  firmness  of  the  crystalline  lens,  on 
account  of  which  it  is  no  longer  able  to  respond  to  the  efiforts  of 
the  ciliary  muscle  to  cause  it  to  assume  an  increased  convexity. 
As  a  result  the  near  point  commences  to  recede  from  the  tenth 
year,  but  presbyopia  cannot  be  said  to  begin  until  the  near  point 
has  receded  beyond  eight  inches,  as  until  that  time  near  ^'ision 
is  but  little  interfered  with. 


What  causes  the  recession  of  the  near  point? 

Lessening  of  the  amplitude  of  accommodation,  as  naturally 
occurs  in  presbyopia. 


What  two  fundamental  reasons  are  there  for  the  oncoming  oJ 
presbyopia? 

Weakening  of  the  ciliary  muscle  and  increase  in  firmness  of 
the  crystalline  lens,  so  that  it  can  no  longer  respond  to  the  action 
of  the  muscle  in  the  effort  to  augment  its  convexity. 


//  there  is  a  tendency  of  the  visual  axes  of  the  two  eyes  to  diverge, 
what  is  the  condition  called?  Suppose  the  deviation  actually  exists, 
then  what  is  the  name  of  the  condition? 

Tendency  to  divergence,  exophoria.  Actual  divergence, 
exotropia. 


When  a  person  of  thirty  years  of  age,  who  is  an  emmetrope  or 
close  thereto,,  has  to  wear  glasses  for  near  vision,  what  condition  is 
probably  present? 

When  a  person  at  this  age  begins  to  need  convex  lenses  for 
reading  we  at  once  suspect  hypermetropia.  But  as  the  question 
intimates  a  condition  of  approximate  emmetropia  the  condition 
must  be  one  of  deficient  or  subnormal  accommodation. 


Pathological  Optometry  221 

When  the  retinal  images  of  an  object  on  the  tivo  retinas  fall  on 
such  retinal  points  that  the  tivo  images  cannot  be  fused  into  one,  what 
is  the  result  and  what  is  the  condition  called? 

Double  vision  or  diplopia;  and  if  there  is  a  deviation  of  one 
eye,  strabismus. 

Define  anaphoria,  cataphoria  and  hyperphoria. 

Anaphoria  is  that  condition  in  which  there  is  a  tendency  for 
the  eyes  to  turn  above  the  normal  position,  as  a  result  of  which 
the  head  must  be  bent  forward. 

Cataphoria  is  that  condition  in  which  there  is  a  tendency  for 
one  visual  line  to  deviate  below  the  other,  and  in  hyperphoria 
above  the  other. 

What  name  is  given  to  that  condition  where  one  eye  is  hyper- 
metropic or  myopic  and  the  other  eye  is  more  so?  When  one  eye  is 
hypermetropic  and  the  other  is  myopic? 

Anisometropia  is  the  general  term  in  use,  although  the  latter 
may  be  called  antimetropia. 


The  punctuni  remotum  of  a  patie?it  twenty  years  old  is  seven 
inches  and  vision  is  improved  by  a  concave  lens.  What  condition 
exists? 

Myopia  of  approximately  5.50  D. 


Hoiv  could  you  objectively  measure  the  deviation  of  a  squinting 
eye? 

One  of  the  most  reliable  methods  is  by  means  of  the  arc  of  a 
perimeter.  The  squinting  eye  should  be  in  the  center  of  the  arc, 
while  the  fixing  eye  should  be  engaged  with  some  distant  object 
across  the  room.  The  angle  of  deviation  is  found  by  moving 
a  lighted  candle  along  the  arc  of  the  perimeter  until  the  reflection 
of  the  flame  appears  to  occupy  that  portion  of  the  cornea  which  is 
directly  over  the  center  of  the  pupil,  when  the  eye  of  the  observer 
is  behind  the  flame.  This  locates  the  optic  axis  of  the  eye  and  the 
amount  of  deviation  can  be  measured  and  read  oft'  the  scale  that 
is  printed  on  the  arc  of  the  instrument. 


228  State  Board  Examinations 

How  would  you  subjectively  measure  the  deviation  of  a  squinting 
eye? 

This  is  possible  only  when  diplopia  can  be  made  evident. 
Ordinarily  in  strabismus  the  squinting  eye  is  arriblyopic  and 
vision  is  monocular;  but  by  exercise  of  the  deviating  eye  to 
improve  its  vision  and  by  placing  a  colored  glass  over  the  fixing 
eye  to  lessen  its  domination,  it  may  become  possible  for  the 
patient  to  discern  two  lights.  When  once  this  is  accomplished 
there  is  no  difificulty  in  measuring  the  deviation  by  the  prism 
that  is  required  over  the  squinting  eye  with  its  base  opposite 
to  the  deviation  that  will  fuse  the  two  lights. 


What  would  lead  to  a  suspicion  of  paralytic  strabismus? 

When  there  is  limitation  of  movement  of  eye  in  one  direction. 

Diplopia,  which  is  confined  to  one  portion  of  the  field  and 
is  increased  the  more  the  eyes  are  turned  in  this  direction. 

Secondary  deviation  of  the  sound  eye  exceeding  the  primary 
deviation  of  the  affected  eye. 

A  strabismus  that  is  noticeable  onh'  in  certain  positions. 


What  are  the  conditions  in  the  following  cases:  Parallel  light 
is  focussed  on  the  retina;  in  front  of  the  retina;  behind  the  retina; 
part  focussed  in  front  of  the  retina  and  part  behind? 

Emmetropia,  myopia,  hypermetropia,  astigmatism. 


What  is  the  difference  in  meaning  of  anaphoria  and  hyper- 
phoria, and  can  the  two  conditions  be  present  at  the  same  time? 

Anaphoria  signifies  an  upward  tendency  of  both  eyes  to- 
gether, the  visual  lines  remaining  parallel  to  each  other. 

Hyperphoria  signifies  a  tendency  of  the  visual  line  of  one 
eye  to  place  itself  above  that  of  the  other,  thus  causing  a  de- 
parture from  parallelism  of  the  \-isual  lines. 

It  is  evident  that  these  two  conditions  could  not  exist  in 
the  same  case  at  the  same  time. 


Pathological  Optometry  229 

What  must  be  the  character  of  the  incident  rays  of  light  in 
order  that  they  may  focus  on  the  retina  when  it  is  situated  nearer 
than  the  principal  focus  of  the  dioptric  system? 

The  rays  must  be  convergent  as  in  hyper metropia,  where 
they  are  made  so  by  the  correcting  convex  lens. 


What  must  he  the  character  of  the  incident  rays  of  light  in 
order  that  they  may  focus  on  the  retina,  when  it  is  situated  beyond 
the  principal  focus  of  the  dioptric  system  of  the  eye? 

The  rays  must  bs  div^ergent  as  in  myopia,  where  they  are 
made  so  by  the  correcting  concave  lens. 


What  is  the  condition  of  hyper  metropia  luhen  the  accommodation 
conceals  a  part  of  the  error,  and  what  term  is  applied  to  the  part 
of  the  error  not  so  concealed? 

Latent  when  concealed  by  the  accommodation  and  manifest 
when  not  concealed. 

-  .12  D.  sph.  =   +  .25  D.  cyl.  axis  140° 


What  will  be  the  refractive  condition  of  the  two  principal 
meridians  of  an  eye  requiring  the  above? 

.12  D.  hypermetropic  in  the  50th  meridian  and  .12  myopic 
in  the  140th  meridian. 

What  kind  of  astigmatism  will  cylinders  correct,  and  what  kind 
will  they  not  correct? 

In  regular  astigmatism  in  which  there  are  two  principal 
meridians  at  right  angles  to  each  other,  one  of  least  and  the  other 
of  greatest  refraction,  cylinders  supply  the  needed  power  in  the 
desired  meridian  to  produce  equalization. 

But  no  glass  can  be  ground  to  correct  irregular  astigmatism, 
in  which  there  is  a  difference  in  power  in  different  parts  of  the 
same  meridian. 

Name  the  two  spherical  errors  of  the  eye  and  state  how  they  are 
corrected? 


230  State  Board  Examinations 

Hypcrnictropia,  in  which  there  is  ^issumed  to  be  a  deficiency 
of  refractive  power,  and  is  corrected  by  a  convex  lens  to  supple- 
ment the  deficiency;  and  myopia,  in  which  there  is  an  excess  of 
refractive  power  and  is  corrected  by  a  concave  lens  to  reduce 
the  excess. 

What  is  the  effect  of  hypermetropia  -on  the  accommodation? 

In  hypermetropia  uncorrected,  there  is  a  constant  tax  or 
strain  on  the  accommodation  to  make  up  for  the  deficiency  of 
refractive  power,  causing  symptoms  of  asthenopia,  as  the 
accommodation  is  called  upon  to  do  more  work  than  in  the 
emmetropic   eye. 

What  is  the  effect  of  myopia  on  the  accommodation. 

In  myopia  there  is  an  overplus  of  refractive  power,  on  which 
account  the  eye  is  adapted  for  near  vision,  and  the  accommoda- 
tion is  called  upon  to  do  much  less  work  than  in  emmetropia. 


What  is  meant  by  the  term  spasm  or  cramp  of  the  accom- 
modation? 

A  persistent  contraction  of  the  ciliary  muscle,  which  fails 
to  relax,  even  when  there  is  no  need  for  its  contraction. 


What  is  the  difference  between  subnormal  accommodation  and 
subnormal  range  of  accommodation? 

By  subnormal  accommodation  the  writer  would  understand 
that  the  power  or  amplitude  of  accommodation  was  below  the 
normal  standard  for  that  particular  age. 

By  subnormal  range  of  accommodation  we  would  under- 
stand that  the  distance  between  near  and  far  points  is  less  than 
normal. 

What  is  meant  by  an  ^'error  of  refraction'  of  the  human  eye? 

The  refraction  of  the  eye  is  its  optical  condition  or  its  action 
on  the  rays  of  light  that  enter  it.  When  refraction  is  normal 
parallel  rays  are  focused  on  the  retina  with  the  accommodation 
at  rest.  Any  departure  from  this  normal  refraction,  when  the 
rays  are  not  so  focused,  is  known  as  an  error  of  refraction. 


Pathological  Optometry  231 

What  kind  of  ametropic  eyes  have  normal  vision  or  better? 

Cases  of  simple  hypermetropia  of  not  too  high  degree. 
Here  the  accommodation  is  easily  able  to  overcome  the  defect, 
and  in  connection  with  the  contraction  of  the  pupil  that  is 
sympathetically  produced,  the  vision  is  thereby  made  good, 
sometimes  even  sharper  than  normal. 


Why  are  cases  of  anisometropia  usually  hard  to  fit? 

In  favorable  cases  where  the  difference  between  the  two 
eyes  is  not  great,  the  correcting  lenses  afford  good  sight  in  both 
eyes  and  comfortable  binocular  vision  is  the  result.  But  in 
many  cases  the  effect  of  correction  is  a  source  of  annoyance  and 
confusion. 

The  effect  of  the  two  different  lenses  on  the  apparent  size 
of  objects  must  be  considered.  For  instance  if  one  eye  is  hyper- 
metropic and  the  other  myopic,  the  convex  lens  for  the  first  eye 
causes  an  apparent  increase  in  the  size  of  the  object,  while  the 
concave  lens  for  the  second  eye  makes  the  object  appear  smaller. 
While  each  of  these  retinal  images  may  be  distinct,  yet  on  account 
of  the  difference  in  their  size  there  is  difficulty  in  fusing  them,  or 
if  fused  it  is  at  the  expense  of  strain. 

If  one  crystalline  lens  has  been  removed  for  cataract,  on 
account  of  the  strength  of  the  lens  that  will  be  required  (+  10  D. 
or  over),  the  patient  is  oftentimes  more  comfortable  if  the  aphakic 
eye  be  left  uncorrected,  that  is  provided  the  other  eye  has  fair 
vision. 

Another  source  of  trouble  is  the  prismatic  effect  of  the  dif- 
ferent lenses.  In  converging  and  looking  through  the  lenses  to 
the  inside  of  the  optical  center,  the  convex  lens  will  show  a  pris- 
matic effect  base  out  and  the  concave  lens  a  prismatic  effect  base 
in.  But  this  disturbance  is  the  more  noticeable  when  looking 
above  or  below  the  optical  centers  of  the  lenses  than  sideways. 

The  older  the  patient  the  more  discouraging  is  the  effort  to 
correct  anisometropia. 

Define  three  kinds  of  asthenopia. 

Accommodative  asthenopia,  due  to  an  overtaxing  of  the 
accommodation  as  in  hypermetropia. 


232  State  Board  Examinations 

Muscular  asthenopia,  due  to  an  overtaxing  of  the  conver- 
gence as  in  myopia. 

Retinal  asthenopia,  where  there  is  hyper-sensitiveness  of  the 
retina  and  suffering  is  caused  by  exposure  to  light. 


How  may  astigmatism  of  one  kind  he  changed  into  that  of 
another? 

In  simple  hypermetropic  astigmatism,  spasm  of  accommoda- 
tion transposes  the  case  into  one  of  apparent  simple  myopic 
astigmatism  with  the  defect  in  the  meridian  at  right  angles. 

Then,  too,  with  the  advance  of  age  the  addition  of  the  neces- 
sary convex  lens  to  correct  the  presbyopia,  changes  a  case  of 
simple  hypermetropic  astigmatism  and  a  case  of  simple  myopic 
astigmatism  into  one  of  mixed  astigmatism. 


How  do  some  people  wrongly  understand  the  word  squint? 

The  terms  squint  and  strabismus  are  used  to  describe  the 
same  condition,  but  the  popular  understanding  of  squint  is  the 
act  of  half  closing  the  lids  in  the  effort  to  see  or  to  protect  the 
eyes  from  excessive  glare. 

What  is  the  differe?ice  between  tonic  and  clonic  spasm  of  the 
ciliary  muscle? 

A  tonic  spasm  is  one  that  is  constant  or  continuous,  while  a 
clonic  spasm  is  intermittent. 


What  is  the  difference  bettoeen  concomitant  and  paralytic 
strabismus? 

In  concomitant  strabismus,  the  squinting  eye  maintains  the 
same  relation  with  the  fixing  eye  and  follows  it  in  all  of  its  move- 
ments. 

In  paralytic  strabismus,  the  affected  eye  is  unable  to  turn  in 
the  direction  of  the  paralyzed  muscle,  and  hence  cannot  follow 
the  movements  of  the  fixing  eye. 


When  woidd  you  consider  the  chances  good  for  the  disappearance 
of  squint  as  the  result  of  wearing  glasses? 


Pathological  Optometry  233 

When  the  squint  is  convergent  and  caused  by  hypermetropia, 
when  the  error  is  fully  corrected,  and  most  important  when  the 
glasses  are  put  on  at  the  very  commencement  of  the  squint  and 
worn  constantly. 

Name  the  different  reasons  that  are  held  in  regard  to  cause  of 
squint. 

These  may  be  intrinsic  and  extrinsic. 

The  intrinsic  causes  are  errors  of  refraction, ?Lsew\denced  by  the 
convergent  strabismus  of  hypermetropia  and  the  divergent  stra- 
bismus of  myopia;  and  impaired  vision,  as  shown  by  the  strabis- 
mus that  follows  amblyopia  and  opacities  of  the  refracting  media. 

The  extrinsic  causes  are  difference  in  length  or  strength  or 
innervation  of  the  muscles;  variations  in  pupillary  distance, 
in  shape  of  eyeball  and  in  divergence  of  orbits;  and  impair- 
ment of  fusion  faculty. 

What  influence,  if  any,  has  the  correction  of  errors  of  refraction 
on  muscular  deficiencies? 

When  esophoria  exists  with  hypermetropia,  the  correction  of 
the  latter  by  convex  lenses  has  a  favorable  effect  upon  the  muscu- 
lar anomaly;  but  if  exophoria  is  present,  the  convex  lenses  would 
aggravate  it. 

If  exophoria  occurs  in  connection  with  myopia,  the  correction 
of  the  latter  by  concave  lenses  has  a  favorable  effect  upon  the 
outward  deviation;  but  if  exophoria  is  present,  the  concave 
lenses  would  make  it  worse. 


Can  a  myope  have  a  visioji  of  20/20  or  Jaeger  1  without  glasses 
under  any  circumstances?  What  would  be  the  visual  acuity  of  a 
myope  of  2  D.  and  of  6  D.? 

Inasmuch  as  myopia  always  impairs  the  acuteness  of  vision, 
it  is  not  possible  for  a  myope  to  have  the  normal  acuity  of  20  20, 
but  Jaeger  1  (which  refers  to  the  small  size  reading  type)  could 
easily  be  read  if  held  within  the  far  point,  the  higher  the  amount 
of  myopia  the  more  this  point  is  restricted. 

In  high  myopia  even  with  glasses  of  full  correction,  it  is  not 
always  possible  to  afford  a  vision  of  20/20,  on  account  of  the  dis- 


234  State  Board  Examinations 

turbance  to  the  retina  from  the  stretching  and  the  diminishing 
effect  of  the  strong  concave  lenses. 

The  visual  acuity  of  a  myope  of  2  D.  would  probably  be 
reduced  to  20/200  or  one-tenth,  and  of  6  D.  to  6  200  or  one-thir- 
tieth. 

An  emmet  rope  aged  60  has  had  his  crystalline  lens  removed 
for  cataract.  What  glass  would  you  give  him  for  reading  and  what 
glass  for  distant  vision?  Could  he  see  clearly  ivith  either  glass  at  a 
meter? 

For  distant  vision,  the  lens  needed  would  be  about  10  D. 
For  reading,  inasmuch  as  an  aphakic  eye  is  totally  devoid  of  ac- 
commodation, the  lens  must  have  a  focal  distance  that  will  cor- 
respond with  the  distance  at  which  the  person  desires  to  see.  If 
this  is  at  ten  inches,  the  necessary  addition  would  be  +  4  D.,  or 
a  lens  of  14  D.  for  use  at  ten  inches. 

Somewhat  of  an  artificial  accommodation  can  be  produced  by 
moving  the  lens  closer  to  or  farther  from  the  eye.  As  it  is  moved 
farther  away  the  effective  power  of  the  lens  is  increased. 

If  he  had  a  pair  for  distance  and  a  pair  for  reading,  on  account 
of  his  loss  of  accommodation,  neither  pair  would  answer  at  one 
meter;  but  according  to  the  rule  herein  mentioned  +  1  D.  would 
have  to  be  added  to  his  distance  glasses,  which  would  make  +11 
D.  for  vision  at  one  meter. 


A  child,  aged  12,  has  vision  =  20/30,  hut  with  a  concave  lens 
of  1  D.  it  is  raised  to  20/20.  What  would  you  suspect  and  what  tests 
woidd  you  employ  to  ascertain  the  true  nature  of  his  defect? 

We  would  suspect  that  this  was  not  myopia  at  all,  but  proba- 
bly false  or  accommodative  myopia  due  to  spasm  of  accommoda- 
tion, and  that  perhaps  the  real  condition  of  the  refraction  was 
hypermetropic.  When  vision  is  slightly  impaired  as  in  this  case, 
astigmatism  is  also  to  be  suspected. 

The  fogging  method  should  be  used  and  will  probably  show 
if  there  is  any  latent  hypermetropia  and  also  if  astigmatism  is 
present.  Then  a  careful  test  with  the  retinoscope  should  be  made 
and  a  comparison  of  the  results  obtained  from  the  two  methods 
will  reveal  the  true  nature  of  the  defect. 


Physiological  Optics 

Describe  hi  your  own  language  the  Jniman  eye,  givmg  approx- 
imate measurements  of  the  different  parts,  together  ivith  the  changes 
that  take  place  in  changing  from  distant  to  near  vision. 

There  are  three  coats,  the  sclerotic  and  cornea,  choroid,  iris 
and  ciHary  processes,  and  the  retina.  There  are  three  humors, 
the  aqueous,  crystalHne  and  vitreous. 

In  the  standard  eye  the  nodal  point  is  situated  7  mm.  back 
of  the  cornea  and  15  mm.  in  front  of  the  retina.  Allowing  for 
the  thickness  of  the  coats,  the  anteroposterior  diameter  is  about 
23  mm. 

The  anterior  principal  focus  is  15  mm.  and  its  posterior 
principal  focus  20  mm.,  as  measured  from  the  two  principal 
points  situated  about  2  mm.  back  of  the  cornea. 

The  distance  between  cornea  and  front  of  crystalline  lens 
is  3.6  mm. 

The  distance  between  cornea  and  back  of  crystalline  is 
7.2  mm. 

The  distance  between  cornea  and  center  of  rotation  is 
13.2  mm. 

Distance  between  retina  and  center  of  rotation  is  9  mm. 

In  changing  the  adaptation  of  the  eye  from  a  far  point  to 
a  near  point  the  following  changes  take  place: 

Contraction  of  the  ciliary  muscle. 

The  anterior  surface  of  the  lens  becomes  more  convex  and 
approaches  the  cornea. 

The  posterior  surface  of  the  crystalline  increases  very  slightly 
in  convexity;  while  the  axis  of  the  crystalline  increases,  the  equa- 
torial diameter  diminishes.  The  anterior  chamber  becomes  shal- 
lower at  center  and  deeper  at  periphery.  The  pupillary  edge  of 
iris  is  pushed  forward.  The  iris  usually  contracts,  producing  a 
smaller  pupil. 

What  is  the  dioptric  apparatus  concerned  in  the  static  and  in 
the  dynamic  refraction  of  the  eye? 

235 


236  State  Board  Examinations 

Refraction  of  the  eye  has  reference  to  its  action  on  the  rays 
pf  Hght  that  enter  it,  whether  focusing  on  or  off  the  retina.  If 
the  word  refraction  is  used  alone,  unquaHfied  by  any  adjective, 
it  is  understood  to  be  the  static  refraction  of  the  eye  — that  is, 
with  the  accommodation  at  rest.  When  the  term  dynamic  refrac- 
tion is  used,  we  understand  that  the  refractive  power  of  the  eye 
is  increased  by  the  action  of  the  accommodation. 

In  the  first  condition,  the  dioptric  apparatus  concerned 
would  be  the  cornea,  the  aqueous  humor,  the  crystalline  lens 
and  the  vitreous  humor,  which  are  known  as  the  refracting 
media  of  the  eye.  In  the  second  condition,  the  accommodation 
is  brought  into  play  by  the  action  of  the  ciliary  muscle,  but  this 
really  is  not  an  addition  to  the  dioptric  apparatus,  but  produces 
an  increase  in  the  convexity  and  refractive  power  of  the  crystal- 
line lens,  which  is  one  of  the  media. 


Explain  why  the  meter  angle  is  not  the  same  for  different 
persons. 

The  meter  angle  is  the  angle  formed  by  the  meeting  of  the 
visual  line  of  each  eye  with  the  median  line  when  the  eyes  are 
directed  to  an  object  one  meter  away.  This  angle  is  increased 
as  the  object  of  fixation  is  brought  closer  to  the  eyes. 

It  is  also  evident  that  the  size  of  the  meter  angle  will  be 
affected  by  the  pupillary  distance  or  the  distance  between  the 
visual  lines.  The  narrower  the  pupillary  distance,  the  smaller 
the  angle,  while  the  wider  the  pupillary  distance  the  larger  the 
angle. 

What  are  the  essential  portions  of  the  eye  for  carrying  out  the 
function  of  sight? 

1.  A  contractile  diaphragm,  the  iris,  to  regulate  the 
amount  of  light  admitted  to  the  eye. 

2.  Certain  refracting  media,  the  cornea,  aqueous  humor, 
crystalline  lens  and  vitreous  humor,  which  act  collectively  as  a 
convex  lens  to  focus  the  rays  of  light  upon  the  retina  and  form  an 
image  there. 

3.  A  contractile  body,  the  ciliary  muscle,  which  governs 
the  convexity  of  the  crystalline  lens  and  acts  as  the  adjusting 


Physiological  Optics  237 

screw  of  a  microscope,  to  accommodate  the  eye  for  vision  of  short 
distances. 

4.  A  film  or  plate,  the  retina,  to  receive  the  images  of 
external  objects. 

5.  Communication  with  the  brain  centers  by  means  of  the 
optic  nerve,  which  transmits  the  impressions  formed  on  the 
retina. 


What  would  be  the  effect  if  the  retina  zvas  exposed  to  light 
with  no  refracting  media  in  front  of  it? 

Impressions  of  light  would  be  received,  but  would  afford  no 
idea  of  form  or  outline,  producing  merely  the  sensation  of  con- 
fused light,  amounting  simply  to  the  perception  of  light  from 
darkness. 


What  is  the  action  of  the  eye  on  rays  of  light  entering  it? 
Explain  fully  how  this  action  is  performed  and  mention  the  media 
traversed. 

Passing  from  air  (index  1.00)  into  the  cornea  (index  1.33) 
they  are  very  strongly  converged ;  then  continuing  in  the  aqueous 
humor  which  has  about  the  same  index  (1.33)  and  hence  may  be 
considered  a  continuation  of  the  cornea.  Passing  into  the 
crystalline  lens  which  has  a  higher  index  (1.43)  and  with  a  convex 
anterior  surface,  the  rays  are  still  more  converged  but  not  as 
much  as  on  entering  the  cornea,  because  the  curvature  is  not  so 
great  and  because  the  difference  between  the  aqueous  (1.33)  and 
the  crystalline  (1.43)  is  not  as  great  as  the  difference  between  air 
(1.00)  and  the  cornea  (1.33).  Continuing  then  through  the  more 
refractive  crystalline  (1.43)  to  the  less  refractive  vitreous  (1.33), 
but  through  a  surface  which  is  markedly  convex  towards  the  less 
refractive  medium,  the  rays  suffer  more  convergence  and  pass  on 
to  meet  in  focus  upon  the  retina. 


Explain  fully  the   Helmholtz  and  the    Tscherning   theory   of 
accommodation. 

The  Helmholtz  theory  of  accommodation  assumes  that,  on 
account  of  the  anterior  extremity  of  the  ciliary  muscle  being 


2vS8  Stale  Board  Exanii nations 

allachcd  to  the  firm  sclcro-corncal  junction,  contraction  of  the 
muscle  will  draw  forward  the  anterior  portion  of  the  choroid; 
as  a  result  the  ciliary  processes  and  the  suspensory  ligament  of 
the  lens  would  also  be  drawn  forward,  with  a  consequent  relaxa- 
tion of  the  latter. 

The  crystalline  lens  is  enclosed  in  a  contractile  capsule,  and 
in  youth  when  accommodation  is  most  active  its  substance  is  soft 
or  semi-fluid.  The  tendency  of  such  a  gelatinous  mass  is  always 
to  approximate  the  shape  of  a  sphere  or  globe,  according  to  the 
laws  of  physics,  because  a  fixed  volume  of  matter  presents  its 
smallest  area  of  external  surface  in  this  form,  and  hence  the  sur- 
face-tension of  the  mass  in  connection  with  the  contractibility  of 
the  capsule,  is  constantly  trying  to  reduce  this  surface  area. 
Therefore  under  contraction  of  the  ciliary  muscle  the  ligament 
relaxes  and  allows  the  anterior  surface  of  the  lens  to  advance  with 
a  decided  increase  of  curvature. 

Tscherning  argues  that  accommodation  is  produced  not  by 
relaxation  but  by  increased  tension  of  the  suspensory  ligament 
through  the  agency  of  the  ciliary  muscle  and  that  the  increase 
of  curvature  of  the  anterior  surface  of  the  lens  is  confined  to  the 
portion  near  the  apex  of  the  lens,  the  curvature  diminishing 
rapidly  toward  the  periphery. 


What  is  meant  by  the  dioptric  media  of  the  eye? 

The  word  "dioptric"  is  derived  from  the  Greek  and  means  to 
"look  through."  These  are  the  same  as  the  refracting  media  of 
the  eye,  the  cornea,  aqueous  humor,  crystalline  lens,  and  vitreous 
humor,  which  act  on  and  refract  the  rays  of  light  entering  the  eye 
so  as  to  form  an  image  on  the  retina. 


What  are  Purkinje's  figures?  Draw  a  diagram  illustrating  the 
formation  of  these  figures  (a)  whe^i  the  illuminatioyi  is  directed 
through  the  sclerotic,  (b)  when  the  illumination  is  directed  through 
the  pupillary  space. 

Purkinje  described  an  entoptic  method  of  observation  of  the 
retinal  vessels,  which  was  intended  to  prove  that  the  perceptive 
faculty  for  light  is  located  in  the  outer  portions  of  the  cones. 


Physiological  Optics 


23  > 


A  strong  light  is  focused  upon  the  sclerotic  near  the  cornea 
and  the  transmitted  light  will  cast  shadows  of  the  interxening 
blood-vessels  on  the  outer  layer  of  the  retina.  This  perception  of 
one's  own  blood-vessles  is  possible  because  they  lie  anterior  to  the 
principal  percipient  layer  of  the  retina.  The  disk  cannot  be  seen 
because  it  has  no  percipient  layer,  but  under  favorable  circum- 
stances the  retina  may  be  seen  almost  up  to  the  disk,  including 
the  macula  which  is  surrounded  by  capillary  loops. 


Fig.  ii 

In  a  darkened  room  a  candle  is  held  to  one  side  of  the  eye 
at  an  angle  of  about  30  degrees  with  visual  line  on  one  side,  and 
if  the  observer's  eye  be  at  an  equal  angle  on  the  other  side,  there 
can  be  seen  three  distinct  reflected  images  of  the  candle  flame. 

1.  A  bright  virtual  image  of  the  flame  reflected  from  the 
cornea  acting  as  a  convex  mirror. 

2.  A  virtual  image  of  the  flame  reflected  from  the  anterior 
surface  of  the  crystalline  lens,  also  acting  as  a  convex  mirror. 
This  image  is  larger,  less  distinct  and  not  so  noticeable  as  the  first. 

3.  A  bright  but  small  real  image  reflected  from  the  posterior 
surface  of  the  crystalline,  acting  as  a  concave  mirror. 

The  first  and  second  images  are  upright  and  the  third  is 
inverted. 


240  Slate  Board  Examinations 

The  eye  under  observation  is  now  made  to  change  its  point 
of  sight  from  a  distant  to  a  near  object;  in  other  words,  to  ac- 
commodate, when  it  will  be  seen  that  the  second  image  which  it 
reflected  from  the  anterior  surface  of  the  crystalline  becomes 
smaller  and  clearer,  and  moves  forward  and  toward  the  center 
of  the  pupil;  thus  proving  that  this  anterior  surface  of  the 
crystalline  becomes  more  convex.  Images  1  and  3  are  not  changed, 
thus  proving  that  the  other  surfaces  are  not  affected  by  accom- 
modation. 


What  is  the  axis  of  vision? 

This  is  the  line  which  joins  the  object  with  the  fovea  cen- 
tralis;  it  is  also  known  as  the  visual  line. 


The  eye  is  said  to  be  chromatic,  a?id  yet  this  condition  is  not 
usually  manifest.    Hoiv  can  its  existence  be  shown? 

By  the  use  of  a  cobalt  blue  glass  while  looking  at  a  light. 
This  lens  allows  both  blue  and  red  light  to  pass  through  it,  the 
former  being  most  refracted  and  the  latter  least. 


What  are  the  nodal  points  of  the  eye? 

The  nodal  point  is  located  at  the  center  of  curvature  of  the 
eye,  or  at  its  optical  center,  and  is  the  point  through  which  rays 
pass  without  deviation.  It  may  be  said  to  coincide  with  the 
ape.x  of  the  posterior  surface  of  the  crystalline  lens. 

Every  lens,  strictly  speaking,  has  two  nodal  points,  but  in 
thin  lenses  the  deviation  of  the  secondary  rays  is  so  slight  that 
for  all  practical  purposes  only  one  nodal  point  is  recognized. 

The  first  nodal  point  lies  7.09  mm.  behind  the  anterior  sur- 
face of  the  cornea,  and  the  second  nodal  point  7.46  mm.  behind. 
The  interval  between  the  two  nodal  points  is  so  small  that  they 
can  be  regarded  as  one,  and  its  distance  is  given  as  7.2  mm.  behind 
the  cornea.  The  angle  which  an  object  subtends  at  the  nodal 
point  governs  the  size  of  the  retinal  image. 


How  is  accommodation  accomplished.^ 


Physiological  Optics  241 

By  means  of  the  ciliary  muscle  acting  upon  the  crystalline 
lens  in  such  a  way  as  to  increase  its  convexity.  There  are  two 
theories  of  accommodation  as  promulgated  by  Helmholtz  and 
Tscherning.  According  to  the  first  the  lens  tends  to  assume  a 
spherical  shape  when  allowed,  which  is  accomplished  by  the  action 
of  the  ciliary  muscle  on  the  fibers  of  the  zonula,  so  as  to  permit 
the  lens  to  assume  a  more  spherical  shape.  According  to  the 
second  the  periphery  of  the  lens  is  flattened,  with  the  result  of 
causing  a  bulging  at  the  center. 


What  is  the  optic  axis  of  the  eye? 

An  imaginary  line  that  passes  through  the  apex  of  the  cornea 
and  the  center  of  the  crystalline  lens  to  a  point  on  the  retina  at 
the  center  of  the  fundus. 

Suppose  for  any  reason  an  emmetropic  eye  should  become 
myopic,  what  ivould  he  the  change  in  the  size  of  the  apparent  size 
of  objects? 

The  size  of  the  retinal  image  is  governed  by  the  distance 
between  the  nodal  point  and  the  retina,  that  is,  the  distance  the 
rays  diverging  from  the  nodal  point  must  travel  before  reaching 
the  retina. 

Inasmuch  as  this  distance  increases  in  the  elongated  eye 
of  axial  myopia,  it  follows  that  there  will  be  an  increase  in  the 
apparent  size  of  objects. 

What  is  the  relation  of  the  dioptric  system  of  the  eye  to  the 
retina  in  each  of  the  folloiving  cases:  emmetropia,  myopia,  hyper- 
opia, astigmia? 

In  emmetropia  the  dioptric  system  is  of  such  power  as  to 
focus  parallel  rays  upon  the  retina  with  the  accommodation 
quiescent.  In  myopia  the  dioptric  system  shows  an  excess  of 
power,  causing  parallel  rays  to  focus  in  front  of  the  retina.  In 
hypermetropia  there  is  a  deficiency  of  refractive  power,  allow- 
ing the  focus  of  parallel  rays  to  go  behind  the  retina. 

In  simple  hypermetropic  astigmatism  the  dioptric  power  of 
one  meridian  is  just  right,  and  of  the  other  meridian  deficient. 


242  State  Board  Examinations 

In  simple  myopic  astigmatism,  one  meridian  just  right  and 
the  other  meridian  in  excess. 

In  compound  hypermetropic  astigmatism,  both  meridians 
deficient  but  one  more  so  than  the  other. 

In  compound  myopic  astigmatism,  both  meridians  in  excess 
but  one  more  so  than  the  other. 

In  mixed  astigmatism  one  meridian  deficient  and  the  other 
in  excess. 

What  position  does  an  image  on  the  retina  have  relative  to  the 
object? 

The  reproduction  on  the  retina  of  the  object  seen  is  in  the 
form  of  an  inverted  image,  and  this  image  and  the  object  are 
conjugate  to  each  other. 

What  is  the  dioptric  value  of  1  mm.  variation  in  the  distance 
of  the  image  formed  in  an  eye  with  the  ciliary  at  rest? 

About  3  D.  to  be  added  if  the  optic  axis  is  lengthened,  and 
subtracted  if  the  axis  is  diminished. 


Estimating  roughly,  what  would  he  the  increase  in  the  poiver 
of  an  emmetropic  eye  if  the  radius  of  the  cornea  were  1  mm.  more 
or  less  than  is  actually  the  case? 

In  curvature  ametropia  each  millimeter  of  lengthening  or 
shortening  of  the  radius  of  curvature  is  equivalent  to  about  6  D. 


In  a  certain  eye  the  power  of  the  anterior  surface  of  the  cornea 
is  42  D.,  while  the  total  dioptric  poiver  of  the  eye  is  52  D.  What 
will  be  the  dioptric  power  of  the  eye  if  this  head  is  immersed  in 
water,  the  refractive  index  of  the  cornea  being  considered  the  same 
as  water? 

Refraction  occurs  when  light  passes  from  one  medium  to 
another  of  different  density,  as  long  as  it  remains  in  the  same 
medium  there  can  be  no  refraction.  In  this  case  where  the  eye 
is  immersed  in  water  and  where  the  cornea  and  the  water  have 
the  same  refractive  index,  light,  in  passing  from  the  water  into 
the  cornea  is  practically   traveling  in   the  same   medium,   and 


Physiological  Optics  243 

hence  there  will  be  no  refraction.  The  refractive  power  of  the 
cornea  being  thus  destroyed,  there  is  a  loss  of  42  D.  and  the 
dioptric  power  of  the  eye  is  thereby  reduced  to  10  D.  This 
explains  why  a  swimmer  who  opens  his  eyes  under  the  water  is 
so  intensely  hypermetropic  that  he  is  unable  to  see  objects 
distinctly. 

What  is  chromatic  aberration,  and  hoiv  is  it  detected  in  the 
human  eye? 

Inasmuch  as  the  degree  of  refraction  by  a  prism  varies  with 
the  wave  length,  therefore  refraction  by  spherical  surfaces  causes 
red  to  deviate  the  least  and  violet  the  most,  and  as  a  result  the 
\arious  colors  do  not  focus  at  the  same  point.  This  is  known  as 
chromatic  aberration. 

When  the  eye  accommodates  for  one  set  of  rays,  it  is  out  of 
focus  for  another,  which  tends  to  cause  a  fringe  of  colors  around 
the  image.  This  defect  in  the  normal  eye  is  so  slight  that  the 
brain  fails  to  take  cognizance  of  it  and  it  is  not  noticeable  in 
ordinary  \'ision. 

That  it  does  exist  in  the  eye,  however,  can  be  proven  by 
the  use  of  a  cobalt  lens,  which  is  placed  before  the  eye  while  the 
patient  is  asked  to  look  at  a  luminous  point.  This  substance 
has  the  property  of  intercepting  all  but  the  red  and  blue  rays. 
The  patient  will  see  an  image  with  a  red  center  clearly  defined, 
and  a  periphery  of  blue,  ill  defined,  for  the  reason  that  the  eye 
more  readily  accommodates  itself  for  the  red  rays,  making  their 
focal  point  distinct.  The  blue  rays  being  more  highly  refracted 
come  to  a  sooner  focus,  cross  and  diverge,  giving  rise  to  diffusion 
circles. 

If  a  concave  lens  be  added  to  the  cobalt,  the  blue  rays  will 
be  focused  on  the  retina  while  the  red  will  now  fall  in  diffusion 
circles,  causing  an  image  with  a  blue  and  distinct  center  and  a 
red  and  diffused  periphery. 


Name  the  different  ametropic  conditions  of  the  eye.     Explain 
each  condition,  giving  its  correction  by  lenses. 

Emmetropia   is   an   eye   in   measure,   when   with   a   passive 
accommodation  parallel  rays  are  accurately  focused   upon   the 


244  State  Board  Examinations 

retina;  ametropia  is  a  departure  from  this  condition,  showing 
itself  in  axial  ametropia  (hypermetropia  and  myopia)  and  curva- 
ture ametropia  (astigmatism).  H\permetropia  and  myopia  may 
also  be  due  to  a  diminution  or  increase  of  curvature  of  the 
cornea  or  crystalline.  Presbyopia  is  not  included,  because  it  is 
a  physiological  change  that  comes  on  with  the  advance  of  age. 

Hypermetropia:  On  account  of  shortness  of  the  antero- 
posterior axis  of  the  eyeball,  or  deficiency  of  refractive  power  in 
cornea  and  lens,  parallel  rays  strike  the  retina  before  uniting  in  a 
focus,  making  the  imaginary  focus  behind  the  retina. 

In  order  that  light  may  focus  upon  the  retina  of  a  hyperme- 
tropic eye  the  rays  must  be  convergent  instead  of  parallel. 
There  are  two  ways  in  which  this  can  be  done. 

First.  By  the  use  of  the  accommodation,  which  the  hyper- 
metrope  does  unconscious!}',  but  as  this  is  an  unnatural  use  of 
the  accommodation,  headache  and  asthenopia  are  likely  to  result. 

Second.  Artificially  by  the  use  of  a  convex  lens,  which 
conv-erges  the  rays  before  entering  the  eye. 

Myopia:  On  account  of  the  length  of  the  anteroposterior 
axis  of  the  eyeball,  or  excess  of  refractive  power  in  the  crystalline 
lens  and  cornea,  parallel  rays  are  brought  to  a  focus  too  soon 
and  meet  in  front  of  the  retina. 

In  order  that  the  focus  may  be  thrown  farther  back  to  the 
retina,  the  rays  must  be  divergent  instead  of  parallel. 

The  eye  possesses  no  power  of  its  own  to  accomplish  this, 
but  it  can  be  done  artificially  by  means  of  a  conca^'e  lens  which 
diverges  the  rays  before  entering  the  eye. 

Inasmuch  as  the  rays  from  near  objects  are  divergent,  they 
can  be  focussed  on  the  retina  of  the  myopic  eye,  hence  near  vision 
is  clear  while  distant  vision  is  blurred. 

Astigmatism.  In  this  error  there  is  a  difference  in  the  curva- 
ture of  the  cornea  in  its  several  meridians,  those  of  greatest  and 
least  refractive  power  being  at  right  angles  to  each  other  and 
known  as  the  principal  meridians. 

The  rays  passing  through  the  vertical  meridian  which  is 
normal,  are  focussed  upon  the  retina;  while  the  rays  passing 
through  the  horizontal  meridian  which  show^s  an  excess  in  curva- 
ture, are  brought  to  a  focus  in  front  of  the  retina.  This  represents 
simple  myopic  astigmatism,  and  is  corrected  by  a  concave  cylin- 


Physiological  Optics  245 

der,   which   diverges   the   rays   passing   through    the   horizontal 
meridian  and  throws  them  back  to  the  retina. 

Astigmatism  may  be  simple,  where  one  meridian  is  emme- 
tropic and  the  other  hypermetropic  or  myopic;  compound  where 
both  meridians  are  defective,  but  one  more  so  than  the  other; 
mixed,  where  one  meridian  is  myopic  and  the  other  hypermetropic. 


What  determines  the  visual  acuity  of  an  eye?  What  constitutes 
normal  vision?  Is  normal  vision  always  present  when  refractive 
conditions  are  emmetropic? 

The  acuteness  of  vision  is  determined  by  the  smallest  dis- 
tance between  two  points  at  which  they  can  be  separately  dis- 
tinguished. It  has  been  found  that  the  minimum  visual  angle  for 
seeing  points  should  be  about  one  minute. 

Snellen's  test  types,  which  are  in  constant  use  for  determin- 
ing the  visual  acuity,  are  constructed  of  such  sizes  that  the  whole 
letter  will  subtend  an  angle  of  five  minutes,  and  each  limb  of  the 
letter  (upon  which  its  visibility  depends)  an  angle  of  one  minute. 

The  No.  20  line  when  placed  at  a  distance  of  twenty  feet  will 
subtend  these  angles,  and  hence  when  a  person  can  name  these 
letters  at  this  distance,  we  say  he  possesses  normal  visual  acuity. 

The  eye  may  be  emmetropic  and  a  well  defined  image  formed 
upon  the  retina  at  the  macula,  but  if  this  impression  is  not  con- 
veyed to  the  brain  by  reason  of  any  failure  of  the  function  of  the 
optic  nerve,  or  of  the  retina  or  of  the  centers  in  the  brain,  there 
could  be  no  resulting  vision. 


What  is  the  cause  of  presbyopia?  State  the  functional  dis- 
turbances in  presbyopia. 

The  cause  of  presbyopia  is  a  gradual  lessening  of  the  power 
of  accommodation.  This  is  a  physiological  condition,  and  is 
dependent  upon  a  diminished  elasticity  of  the  crystalline  lens 
and  a  loss  of  contractibility  of  the  ciliary  muscle.  When  the 
amplitude  of  accommodation  falls  below  4.50  D.  or  5  D.  there  is 
not  sufificient  reserve  to  allow  of  comfortable  vision  at  reading 
distance,  and  artificial  assistance  is  called  for. 

The  loss  of  accommodation  in  presbyopia  destroys  the  rela- 


246  State  Board  Examinations 

tion  that  luid  in  earlier  years  existed  between  the  functions  of 
accommodation  and  convergence. 


Is  the  refraction  of  the  eye  affected  by  spasm  of  the  ciliary 
muscle?  What  is  (a)  tonic  spasm  of  accommodation,  (b)  clonic 
spasm  of  accommodation? 

Spasm  of  the  ciliary  muscle  causes  parallel  rays  of  light  to 
come  to  an  earlier  focus,  thus  simulating  myopia.  Even  in  hyper- 
metropia  there  may  be  an  apparent  myopia,  caused  by  the  action 
of  the  muscle  going  beyond  the  limit  and  producing  an  over- 
correction. 

It  is  to  be  understood  that  the  refraction  of  the  eye  is  not 
actually  altered;   the  change  is  only  apparent,  not  real. 

A  tonic  spasm  is  one  that  is  persistent  and  continuous,  while 
a  clonic  spasm  is  intermittent. 


What  causes  diplopia?  Define  and  explain  three  kinds  of 
diplopia. 

When  the  image  is  focused  upon  portions  of  .the  two  retinae 
that  do  not  correspond,  the  brain  is  unable  to  fuse  them,  and 
double  vision  or  diplopia  results.  Diplopia  may  be  produced 
artificially  by  placing  a  prism  before  one  eye,  which  deflects  the 
rays  from  the  macula  of  that  eye,  for  which  purpose  the  prism 
must  not  be  so  weak  as  to  be  easily  overcome  by  a  contraction  of 
the  muscles. 

Homonymous  diplopia  is  that  form  in  which  the  right  image 
is  seen  by  the  right  eye  and  the  left  image  by  the  left  eye. 

It  is  caused  by  an  inward  de\'iation  of  the  eye,  as  in  esophoria. 
In  such  a  case  the  ray  of  light  impinges  upon  the  retina  at  the 
inner  side  of  the  macula,  and  is  referred  in  the  opposite  direction, 
or  outwardly  according  to  the  law  of  projection.  " 

In  heteronymous  diplopia,  the  diplopia  is  crossed,  the  right 
image  belonging  to  the  left  eye  and  the  left  image  to  the  right 
eye.  This  occurs  in  those  cases  of  muscular  imbalance  where  there 
is  an  outward  deviation  of  the  eye;  under  such  circumstances  the 
ray  of  light  strikes  the  retina  at  the  outer  side  of  the  macula,  and 
is  referred  in  the  opposite  direction,  that  is  inwardly  according 
to  the  law  of  projection  and  the  diplopia  thus  produced  is  crossed. 


Physiological  Optics  247 

Diplopia  may  also  be  vertical,  due  to  hyperphoria  or  hyper- 
tropia. 

In  right  hyperphoria,  the  visual  line  of  the  right  eye  tends 
upwards  in  which  case  the  ray  of  light  entering  this  eye  strikes 
the  retina  at  a  point  abov'e  the  macula  and  is  referred  in  the 
opposite  direction  or  downward.  Hence  the  lower  image  would 
belong  to  the  right  eye  and  the  upper  image  to  the  left. 

In  left  hyperphoria  the  visual  line  of  the  left  eye  tends  above 
that  of  the  right,  under  which  circumstances  the  ray  of  light 
impinges  upon  the  retina  at  a  point  above  the  macula  (in  the 
left  eye)  and  is  referred  in  the  opposite  direction  or  downward. 
In  this  form  of  vertical  diplopia  the  lower  image  would  belong 
to  the  left  eye  and  the  upper  to  the  right. 


Which  are  the  meridians  of  greatest  and  least  corneal  curvature 
when  the  concentric  circles  of  Placido's  disk  appear  reflected  as 
horizontal  ellipses? 

The  greater  the  curvature  the  closer  the  lines  of  the  circle 
would  be  brought  together;  therefore  in  this  case  where  the  upper 
and  lower  borders  of  the  circle  are  approximated,  we  would  say 
the  vertical  was  the  meridian  of  greatest  curvature,  and  the  hori- 
zontal the  meridian  of  least  curvature. 


What  is  dynamic  refraction? 

The  refraction  of  the  eye  is  its  action  while  in  a  static  state 
on  the  light  that  enters  it  and  dynamic  refraction  is  when  the 
action  of  the  ciliary  muscle  is  added  to  that  of  the  refraction 
media. 


The  far  point  ivith  a  plus  3.50  lens  in  place  is  at  50  cm.;  and 
the  same  eye  ivith  a  plus  1.5  lens  in  front  of  it  has  the  near  point  at 
20  cm.  What  is  the  refractive  condition  and  what  is  the  amplitude 
of  accommodation? 

If  the  far  point  with  a  +  3.50  D.  lens  is  located  at  50  cm., 
there  would  be  presumably  an  artificial  myopia  of  2  D.,  which 
would  mean  an  overcorrection  of  that  amount.  Therefore,  +  1-50 


248  State  Board  Examinations 

D.  would  be  the  lens  to  make  the  eye  emmetropic  showing  a 
hypermetropia  of  that  amount. 

A  near  point  of  20  cm.  would  indicate  an  amplitude  of  accom- 
modation of  5  D.  but  if  this  was  obtained  with  the  assistance  of 
the  correcting  lens  of  +  1.50  then  the  amplitude  of  accommodation 
of  the  unaided  eye  would  be  3.50  D. 


In  presbyopia  is  it  not  a  fact  that  the  radiating  fibers  of  the 
ciliary  muscles  have  lost  a  part  of  their  elasticity;  they  are  not  so 
elastic  as  when  young.''  Would  this  not  be  a  good  definition  of  pres- 
byopia? 

The  approach  of  presbyopia  is  caused  by  the  lessening  of 
accommodative  power  on  account  of  the  inability  of  the  crys- 
talline lens  to  continue  to  assume  the  increased  convexity  which 
was  so  easily  possible  in  earlier  years.  So  far  all  are  agreed; 
now  then  as  to  the  cause. 

While  it  is  doubtless  true  that  the  radiating  fibers  of  the 
ciliary  muscle  lose  part  of  their  elasticity  this  does  not  enter  into 
the  question,  as  it  is  the  circular  or  sphincter  fibers  that  are 
actively  concerned  in  the  function  of  accommodation. 

Ordinarily  w'e  say  that  the  failure  of  accommodation  that 
underlies  presbyopia  is  due  to  a  loss  of  contractility  of  the  ciliary 
muscle  and  of  elasticity  of  the  crystalline  lens;  but  the  probabili- 
ties are  that  the  latter  is  the  most  important  factor.  Doubtless 
the  muscle  weakens  somewhat,  but  it  is  the  increasing  sclerosis 
of  the  crystalline  which  can  no  longer  respond  to  the  action  of 
the  ciliary  muscle,  that  is  mainly  responsible  for  the  condition 
known  as  presbyopia. 

What  is  the  size  of  the  retinal  image  of  an  object  9  cm.  high  and 
1.5  meters  distant  from  the  eye  of  a  hypermetrope  of  3  D.? 

The  size  of  the  retinal  image  varies  in  different  eyes  on  ac- 
count of  the  varying  distance  of  the  nodal  point  from  the  retina, 
that  is,  on  the  distance  which  the  axial  rays  have  diverged  from 
each  other  after  leaving  the  nodal  point  and  when  they  reach  the 
retina.  The  farther  these  rays  have  to  travel  before  reaching 
the  retina  the  more  they  are  separated  and,  therefore,  the  greater 
the  retinal  area  occupied  by  the  image.  This  explains  why  in  the 


Physiological  Optics  249 

elongated  eye  of  myopia  objects  seem  larger  and  in  the  flattened 
eye  of  hypermetropia  things  are  seen  smaller. 

In  addition  to  its  distance  from  the  nodal  point  the  size  of 
the  retinal  image  depends  upon  the  size  of  the  object  and  its 
distance  from  the  eye. 

The  size  of  the  retinal  image  bears  the  same  relation  to  the 
size  of  the  object  itself  as  the  distance  between  the  nodal  point 
and  the  retina  bears  to  the  distance  between  the  nodal  point  and 
the  object. 

In  an  emmetropic  eye  the  distance  of  the  retina  from  the 
nodal  point  is  15  mm.,  but  in  a  hypermetropia  of  3  D.  that  dis- 
tance is  reduced  to  14  mm. 

The  problem  may  be  expressed  as  follows.  The  size  of  the 
image  is  to  size  of  object  as  image  distance  is  to  object  distance. 
Let  X  represent  the  size  of  the  retinal  image  and  substituting 
figures  we  have 

X  :  90  mm.  :  :  14  mm.  :  1500  mm. 

then  X  =     .-QQ     =  0.84  mm. 

Multiply  size  of  object  (9  cm.)  by  image  distance  (14  mm.) 
and  divide  by  object  distance  (1.5  meters)  and  the  result  is  0.84 
mm.  as  the  size  of  the  retinal  image. 


What  muscles  are  brought  into  play  in  convergence  to  a  point 
80  inches  and  4  inches  away? 

In  convergence  at  80  inches  the  internal  recti  muscles  are 
brought  into  action;  at  4  inches  they  are  supplemented  by  the 
superior  and  inferior  recti. 

Also  in  simple  myopic  astigmatism  complicated  with  presby- 
opia, while  the  concave  cylinder  will  serve  for  distance,  a  convex 
cylinder  at  right  angles  will  be  needed  for  reading. 


What  change  must  he  made  with  incident  parallel  rays  of  light 
so  as  to  have  them  focus  on  the  retina  when  it  is  situated  beyond  the 
principal  focus  of  the  dioptric  system? 

If  the  retina  is  situated  beyond  the  principal  focus  of  the 
dioptric  system,  or  in  other  words  if  parallel  rays  come  to  a 


250  State  Board  Examinations 

focus  too  soon  (as  is  the  case  in  myopia)  they  must  l)e  made 
divergent  before  entering  the  eye  so  as  to  throw  the  focus  further 
back  upon  the  retina  which  can  be  accompHshed  by  means  of  a 
concave  lens  of  the  proper  strength. 


Explain  the  reason  for  the  improvement  in  vision  obtained  by 
the  pinhole  disk. 

In  the  several  forms  of  ametropia  parallel  rays  of  light  can- 
not focus  upon  the  retina  and  as  a  result  the  acuteness  of  vision  is 
impaired.  In  hypermetropia  the  rays  reach  the  retina  before 
coming  to  a  focus,  whereas  in  myopia  they  meet  in  front  of  the 
retina  and  cross  and  diverge;  in  both  cases  the  retina  receives 
circles  of  diffusion.  The  pinhole  disk  cuts  off  the  peripheral  rays 
and  allows  only  the  more  central  ones  to  pass,  and  in  this  way 
reduces  the  amount  of  diffusion  and  affords  the  more  perfect 
image  of  the  central  ray  which  passes  unrefracted.  Of  course,  the 
illumination  is  reduced  by  cutting  off  so  much  light,  but  this  is 
more  than  compensated  for  by  the  improvement  in  the  sharpness 
of  the  retinal  image. 


Explain  the  method  applied  to  ascertain  the  powers  of  abduction 
and  adduction,  sitpraduction  and  infraduction. 

The  duction  tests  consist  in  applying  prisms  as  strong  as  can 
be  borne  with  apices  over  the  muscle  it  is  desired  to  measure. 

The  strongest  prisms  bases  in  which  can  be  overcome  and 
with  which  single  vision  of  a  light  can  be  maintained,  will  repre- 
sent the  power  of  abduction. 

The  strongest  prisms  bases  out  which  can  be  overcome  will 
represent  the  power  of  adduction. 

The  strongest  prisms  bases  down  for  supraduction,  and  bases 
up  for  infraduction. 

The  eye  turns  toward  the  apex  of  the  prism,  and  when  the 
iimit  of  its  duction  power  is  exceeded  the  light  becomes  double. 


Why  is  it  necessary  to  change  occasionally  the  focus  of  glasses 
for  close  range  after  the  patient  has  passed  the  age  of  forty? 


Physiological  Optics  251 

Such  persons  wear  glasses  for  the  correction  of  their  pres- 
byopia, which  is  an  error  of  accommodation,  and  depends  upon 
the  lessened  power  of  this  function  due  to  the  changes  which 
age  brings  on.  As  these  changes  are  progressive  the  amplitude 
of  accommodation  gradually  diminishes  until  it  is  finally  lost 
altogether.  This  necessitates  a  change  of  glasses,  increasing  their 
strength  about  .50  D.  every  two  and  one-half  years. 


What  are  the  effects  of  the  extrinsic  muscles  on  the  relation  of 
the  visual  lines  of  the  two  eyes? 

The  effect  of  the  extraocular  muscles  is  such  as  to  keep  the 
optic  axes  of  the  two  eyes  in  a  proper  relation  to  each  other  in 
all  the  ordinary  movements  of  the  eyes  that  binocular  vision  shall 
always  be  present  no  matter  in  which  direction  the  eyes  may  find 
it  necessary  to  turn. 

What  is  the  posterior  principal  focus  of  the  eye? 

It  is  the  focus  for  parallel  rays  that  enter  the  eye,  and  in  the 
emmetropic  eye  is  located  at  the  retina;  when  such  is  the  case  the 
eye  is  adapted  to  receive  a  clear  image  of  a  distant  object. 

In  hypermetropia  with  the  accommodation  at  rest,  the  prin- 
cipal focus  of  the  eye  is  located  behind  the  retina,  as  a  result  of 
which  the  retinal  image  will  be  blurred.  In  myopia  the  prin- 
cipal focus  of  the  eye  lies  in  front  of  the  retina,  and  again  the 
image  on  the  retina  will  be  blurred. 


What  will  be  the  height  of  the  image  of  a  6-foot  man  on  the 
retina  of  an  emmetropic  eye  if  the  man  is  100  feet  aivay? 

The  angle  formed  at  the  nodal  point  governs  the  size  of  the 
image  on  the  retina,  or  we  may  express  it  in  this  way,  that  it 
depends  upon  the  distance  between  the  nodal  point  and  the  retina. 
The  rays  meet  at  the  nodal  point  and  then  they  begin  to  diverge. 
The  farther  away  the  retina,  the  more  these  rays  diverge,  and 
therefore  the  greater  the  area  on  the  retina  occupied  by  the 
image.  This  explains  why  in  myopia,  where  the  retina  is  farther 
from  the  nodal  point  the  image  is  larger,  and  in  hypermetropia 
where  the  retina  is  nearer  to  the  nodal  point,  the  image  is  smaller. 


252  State  Board  Examinations 

In  calculating  the  size  of  the  retinal  image  it  is  to  be  remem- 
bered that  its  size  bears  the  same  relation  to  the  size  of  the 
object  as  the  distance  of  the  retina  from  the  nodal  point  (which 
means  the  distance  of  the  image  from  the  nodal  point)  bears  to 
the  distance  of  the  object  from  the  nodal  point,  which  may  be 
expressed  in  the  following  proportion: 
Size  image    :    Size  object    ::    Distance  image    :    Distance  object. 

Allowing  15  mm.  as  the  estimated  distance  of  the  nodal 
point  from  the  retina  and  substituting  figures  in  this  case,  we 
have : 

6  feet  100  feet 

^  ■   or  1800  mm.    '•'         "^"^"    '    or  30,000  mm. 
orx  =  2  7  /30  of  a  millimeter,  which  is  the  height  of  the  retinalimage. 


What  glasses  must  he  prescribed  for  tJiose  icho  no  longer  possess 
the  function  of  accommodation? 

This  question  no  doubt  has  reference  to  old  age,  in  which, 
according  to  natural  laws,  the  power  of  accommodation  has  been 
entirely  lost. 

In  these  cases  there  is  usually  more  or  less  of  acquired  hyper- 
metropia,  due  to  the  lessening  of  refractive  power  as  a  result  of 
the  senile  changes.  This  will  call  for  correction  and  in  addition 
another  pair  of  glasses  must  be  given  for  reading,  about  2.50  D. 
or  3  D.  stronger  than  the  distance  pair;  or  preferably  a  pair  of 
bifocals. 

In  eyes  which  are  strictly  emmetropic  and  in  which  the 
function  of  accommodation  has  been  lost,  the  glass  that  is  given 
must  correspond  with  the  desired  reading  distance;  if  at  13 
inches,  3  D.;  if  at  10  inches,  4  D.,  and  so  on. 


When  is  hypermetropia  said  to  he  ahsoliite? 

When  it  cannot  be  neutralized  by  the  accommodation, 
either  because  the  defect  is  of  too  high  degree  or  because  the 
accommodative  power  has  been  lost,  as  in  old  age.  Under  such 
conditions  vision  is  impaired  at  all  distances,  but  especially  near 
vision. 


Physiological  Optics  253 

When  is  hypermetropia  said  to  he  facultative? 

When  it  can  be  neutralized  by  the  accommodation.  His 
vision  is  good  either  with  or  without  a  convex  lens.  This  is  the 
condition  usually  found  in  early  life. 


What  is  the  difference  between  regular  and  irregular  astigma- 
tism? 

Regular  astigmatism  is  due  to  a  toric  shape  of  cornea  or 
crystalline,  the  curvature  being  regular  from  the  minimum  to 
the  maximum  meridians,  and  the  defect  can  be  readily  corrected 
by  cylindrical  lenses. 

Irregular  astigmatism  is  caused  by  unevenness  of  the  surface 
of  the  cornea,  there  being  a  difference  in  refraction  in  different 
parts  of  the  same  meridian.  As  a  result  of  this  distortion  of  the 
cornea,  an  imperfect  retinal  image  is  formed  and  cylindrical 
lenses  are  of  little  value. 


What  is   the  difference  in   meaning   between   esophoria   and 
esotropia? 

Esophoria  signifies  a  tendency  to  inward  deviation,  esotropia 
an  actual  turning  of  the  eye  inwards. 


Which  will  produce  the  poorest  visual  acuity,  an  error  of  2  D. 
spherical  or  2  D.  astigmatically? 

If  the  error  is  myopic,  it  is  probable  that  the  spherical  error 
will  impair  vision  the  most.  But  if  the  error  is  hypermetropic 
of  not  too  high  degree  it  is  probable  the  accommodation  can 
more  completely  overcome  the  spherical  error,  and  hence  in 
this  case  it  is  likely  that  the  astigmatic  error  will  produce  the 
poorest  vision. 

In  measuring  the  amplitude  of  accommodation  with  a  reading 
chart  why  is  the  test  not  exact? 

Because  for  short  distances  the  type  is  too  large  and  because 
a  person  becomes  familiar  with  certain  words  by  their  appearance 
as  to  the  number  of  letters  composing  them  and  the  shape  of 


254  State  Board  Examinations 

such  letters,  so  that  he  is  able  to  make  a  very  good  guess  at 
words  e\en  when  he  docs  not  see  the  letters  plainly. 


What  is  hyperphoria  and  what  is  the  position  of  the  correcting 
prisms/ 

Hyperphoria  is  the  term  used  to  indicate  a  tendency  of  the 
visual  line  of  one  eye  to  place  itself  above  that  of  the  other. 
This  upward  tendency  may  affect  either  eye,  and  hence  we  have 
right  hyperphoria  or  left  hyperphoria. 

The  position  of  the  correcting  prism  is  base  down  over  the 
hyperphoric  eye,  or  base  up  over  the  other  eye,  or  di\'ided  be- 
tween the  two  eyes  in  these  positions. 


When  the  refraction  of  the  two  eyes  differs  what  term  is  applied 
to  the  condition? 

Anisometropia  is  the  usual  term,  although  the  word  anti- 
metropia  is  also  used.  It  is  seldom  we  find  the  two  eyes  exactly 
alike,  but  the  term  is  applied  only  when  the  difference  is  great 
enough  to  receive  consideration. 

Anisometropia  is  usually  a  congenital  condition,  but  it  may 
also  be  due  to  the  natural  progress  of  a  myopia,  to  operation  or 
injury,  and  to  changes  in  corneal  curvature. 


If  the  punctunt  proximnm.  in  emmetropia  is  at  33  cm.  when 
the  eyes  are  being  assisted  by  +  1.50  D.  lenses,  what  is  the  amplitude 
of  accommodation  and  what  lenses  should  be  prescribed  for  reading 
at  33  cm.,  so  as  to  keep  one-third  of  the  accommodation  in  reserve? 

A  near  point  of  ^2>  cm.  represents  an  amplitude  of  accom- 
modation of  3  D.  and  as  this  is  accomplished  by  the  assistance 
oi  a  -\-  1.50  D.  lens  the  natural  amplitude  of  accommodation 
would  be  1.50  D. 

In  order  to  read  at  2>i  cm.  3  D.  of  power  is  required,  and  in 
order  that  one-third  of  this  person's  accommodation  should  be 
kept  in  reserve,  he  can  use  only  1  D.  of  his  ow^n  accommodation 
and  the  balance  must  be  supplied  by  a  +  2  D.  lens. 


Physiological  Optics  255 

When  the  eye  turns  up  and  in,  by  what  muscles  is  it  controlled? 

Superior  rectus  and  internal  rectus,  the  upward  movement 
being  probably  assisted  by  the  inferior  oblique. 


In  the  static  eye  in  the  case  of  an  emmetrope,  what  will  be  the 
effect  on  the  retinal  image  of  wearing  a  -\-  1  D.  cylinder,  axis  180°? 

To  distort  the  image,  elongating  it  in  the  vertical  meridian 
or  at  right  angles  to  axis  of  cylinder. 


What  is  the  condition  of  the  muscles  of  the  eyes  in  each  of  the 
following  cases:    Orthophoria,   esophoria,   exophoria,  hyperphoria? 

Orthophoria,  muscles  properly  balanced;  esophoria,  ten- 
dency to  overconvergence ;  exophoria,  tendenc}^  to  over-diver- 
gence; hyperphoria,  a  tendency  of  one  visual  line  above  the 
other. 

In  esophoria  the  correcting  prism  is  placed  base  out,  in 
exophoria  base  in,  and  hyperphoria  base  down  over  the  hyper- 
phoric  eye. 

What  is  spasm  of  the  ciliary  muscle? 

An  involuntary  cramp  or  contraction  of  the  ciliary  muscle. 
This  is  the  term  applied  to  an  overaction  of  the  accommodation, 
occurring  especially  in  young  people  in  the  effort  to  overcome 
a  condition  of  hypermetropia  or  hypermetropic  astigmatism  and 
makes  the  eye  apparently  and  subjectively  myopic,  thus  leading 
the  inexperienced  optometrist  sometimes  into  the  error  of  pre- 
scribing concave  glasses. 

It  is  more  apt  to  occur  in  patients  whose  nervous  system  is 
broken  down  and  oftentimes  in  those  with  a  relatively  weak 
accommodation. 

The  usual  symptoms  are  photophobia,  lachrymation,  pain, 
contracted  pupils  and  congestion  of  the  eye,  together  with  the 
appearance  of  myopia. 


How  is  spasm  cured? 

The  first  step  in  the  treatment  is  the  removal  of  the  cause  if 
it  can  be  ascertained,  as  the  correction  of  any  existing  hyperme- 


256  State  Board  Examinations 

tropia  or  astigmatism.  Or  convex  lenses  for  fogging  to  induce 
relaxation  of  the  accommodation,  a  weaker  pair  for  distance  and 
stronger  for  reading.  Rest  of  the  eyes  and  temporary  abstinence 
from  reading  and  sewing  should  be  advised. 


What  is  diplopia  and  what  is  the  explanation? 

Diplopia  is  double  vision,  two  images  being  seen  instead  of 
one,  and  is  due  to  the  fact  that  the  images  are  not  formed  on 
corresponding  parts  of  the  two  retinae. 


What  is  the  character  of  the  difference  in  direction  of  the  eyes 
if  diplopia  is  homonymous? 

Esophoria,  or  inward  deviation. 


What  is  mojiocidar  diplopia  and  what  is   its  explanation? 

Multiple  vision  in  one  eye,  usually  due  to  a  slight  difference 
in  the  index  of  refraction  of  the  several  main  segments  of  the 
crystalline  lens,  each  of  which  gives  rise  to  a  separate  retinal 
image. 

In  emmetropia  these  images  are  so  close  that  they  are  fused 
into  one,  but  in  ametropia,  where  the  retina  is  not  at  the  position 
of  the  average  focus,  vision  is  multiple. 


What  is  heterophoria  and  how  does  it  differ  from  diplopia? 

Heterophoria  is  the  term  used  to  include  all  those  conditions 
in  which  there  is  a  tendency  to  depart  from  the  normal  muscular 
balance,  which  nature  is  able  to  compensate  for  and  keep  latent, 
but  which  is  demonstrable  by  the  usual  tests. 

Diplopia  means  double  vision,  and  is  produced  by  and  is  a 
symptom  of  heterotropia,  a  term  used  to  include  all  those  con- 
ditions in  which  nature  is  unequal  to  the  task  of  maintaining  its 
desire  for  single  vision. 

What  is  anisometropia? 

This  term  is  applied  to  that  condition  of  the  eyes  where  the 
refraction  is  unequal.      In  a  restricted  sense  of   the  word  we 


Physiological  Optics  257 

seldom  find  two  eyes  exactly  alike,  but  the  term  is  used  only 
when  the  difference  is  great  enough  to  be  taken  into  account. 
The  usual  condition  is  where  the  character  of  the  refraction  is 
the  same  in  both  eyes,  varying  only  in  degree.  Where  the 
character  of  the  refraction  varies  in  the  two  eyes,  that  is  one  eye 
hypermetropic  and  the  other  myopic,  the  term  antimetropia  is 
sometimes  used. 

What  conditions  produce  diplopia? 

Diplopia  occurs  when  the  visual  axes  are  directed  so  that  the 

image  of  the  object  does  not  fall  upon  identical  parts  of  both 

.  retinae.    Any  disturbance  of  the  extra-ocular  muscle  balance,  as 

in  heterotropia,  or  even  in  heterophoria  may  cause  this  condition, 

and  sometimes  it  is  due  to  faulty  innervation. 


Which  surface  of  the  cornea  has  the  greater  refractive  power, 
and  why? 

The  refracting  power  of  the  cornea  lies  chiefly  in  its  anterior 
surface.  The  effect  of  the  posterior  surface  is  neutralized  by  being 
in  contact  with  the  aqueous  humor  which  has  the  same  index  of 
refraction,  and,  therefore,  the  aqueous  may  be  considered  as  a 
continuation  of  the  cornea. 


How  can  the  degree  of  convergence  he  determined  for  any  given 
working  distance,  and  for  any  given  pupillary  distance? 

The  rule  is  to  divide  the  pupillary  distance  by  the  unit  of 
displacing  power  at  the  given  working  distance. 

If  we  take  a  working  distance  of  13  inches  (which  is  one-third 
of  a  meter)  the  displacement  would  be  3.33  mm.,  based  on  the 
unit  or  standard  of  displacement  of  10  mm.  for  each  meter  of 
distance.  We  will  assume  the  pupillary  distance  is  2^  inches, 
which  is  equivalent  to  64  mm.  Then  the  number  of  degrees  of 
convergence  in  a  patient  with  the  pupillary  and  working  distances 
mentioned  above  is  found  by  dividing  3.33  into  64,  and  the  result 
is  19.21  degrees  of  convergence. 


What  is  the  dioptric  power  of  the  anterior  surface  of  the  cornea, 
and  what  is  its  power  as  a  convex  mirror? 


258  State  Board  Examinations 

In  order  to  find  the  refractive  power  of  the  cornea  we  divide 

its  index  of  refraction,  less  unity,  into  its  radius  of  curvature,  as 

follows : 

8  mm. 


(1.33—1) 


=  24  mm. 


24  mm.  is  its  focal  length  and  we  find  its  refractive  or  dioptric 
power  by  dividing  this  into  1000  mm.,  and  the  result  is  41  D. 

Assuming,  as  we  have  done  in  the  above  example,  that  the 
radius  of  curvature  is  8  mm.  and  as  the  focus  of  a  mirror  is  one- 
half  its  radius,  its  focal  length  as  a  mirror  is  4  mm.,  and  its  power 
is  found  by  dividing  this  into  1000  mm.,  the  result  being  250  D. 


What  is  difference  between  binocular  vision  and  fusion? 

They  mostly  convey  the  same  meaning;  but  a  person  with 
binocular  vision  whose  fusion  sense  is  but  feebly  developed  will 
under  unfavorable  circumstances  abandon  the  efTort  and  drop  into 
monocular  vision.  While  another  person  whose  fusion  sense  is 
well  developed  will  have  such  an  intense  tendency  to  binocular 
vision  that  nothing  will  cause  him  to  abandon  it. 


What  is  the  name  given  to  that  part  of  the  retina  in  which  visual 
acuity  is  the  sharpest? 

Macula  lutea,  or  yellow  spot  in  general  and  fovea  centralis 
in  particular. 

What  would  be  the  change  in  the  refraction  of  the  cornea  if  its 
radius  of  curvature  should  be  changed  about  1  mm.? 

It  depends  upon  whether  the  change  of  radius  was  in  the 
direction  of  an  increase  or  a  decrease.  If  the  radius  of  curvature 
was  increased  1  mm.  there  would  be  a  decrease  in  refractive  power 
of  approximately  5  D.  Whereas,  if  the  radius  of  curvature  of  the 
cornea  was  lessened  1  mm.  there  would  be  an  increase  of  refractive 
power  of  nearly  7  D. 

What  would  be  the  change  in  the  dioptric  power  of  the  crystalline 
lens  if  the  radius  of  curvature  shoidd  be  changed  1  mm.? 


Physiological  Optics  259 

Here  the  two  surfaces  of  the  crystalline  must  be  taken  into 
account  in  considering  its  dioptric  power. 

If  the  anterior  surface  showed  an  increase  in  radius  of  1  mm. 
there  would  be  a  loss  in  power  of  1  D.  If  this  surface  showed  a 
decrease  in  radius  of  1  mm.  there  would  be  an  increase  in  refrac- 
tive power  of  1  D. 

If  the  posterior  surface  showed  an  increase  in  radius  of  1 
mm.  there  would  be  a  loss  of  power  of  2  D.  If  this  surface 
showed  a  decrease  of  1  mm.  there  would  be  an  increase  in  refrac- 
tive power  of  3  D. 

If  the  radius  of  the  two  surfaces  was  changed  1  mm.  the 
resultant  change  in  "dioptric  power  can  be  figured  from  above. 


The  distance  between  the  centers  of  the  two  eyes  when  they  are 
looking  into  distance  is  62  mm.  If  the  glasses  used  are  placed  about 
12  mm.  in  front  of  the  cornea  and  the  object  of  regard  is  at  a  distance 
of  20  inches,  what  must  be  the  pupillary  distance  of  the  glasses? 

An  optical  writer  figures  it  as  follows:  The  centers  of  rotation 
are  13  mm.  back  of  cornea,  therefore,  the  distance  from  these 
centers  to  the  lenses  would  be  25  mm.,  or  1  inch.  Then  the  lenses 
would  be  19  inches  from  the  object,  and  the  p.  d.  of  the  glasses 
would  be  19/20  of  62  mm.  or  59  mm. 


At  what  ages  does  the  accommodation  of  the  eye  being  to  decrease? 

At  ten  years,  continuing  gradually  to  decrease  until  it  is 
entirely  lost  in  old  age. 


What  is  the  difference  in  the  function  of  the  blind  spot  and  of 
the  yellow  spot? 

The  blind  spot  is  at  the  entrance  of  the  optic  nerve,  and  as  it 
is  insensible  to  light  it  cannot  be  said  to  have  any  function. 

The  function  of  the  retina  is  to  receive  the  images  of  external 
objects  and  transmit  the  impressions  to  the  brain.  The  yellow 
spot  is  that  part  of  the  retina  that  is  most  highly  developed  for 
this  purpose. 


260  State  Board  Examinations 

Why  is  the  pupillary  distance  less  for  near  glasses  than  for 
distant  ones? 

Because  the  eyes  turn  in  in  response  to  the  increased  con- 
vergence that  is  necessary  to  maintain  binocular  vision  at  near 
points,  and  in  so  doing  the  pupillary  distance  is  necessarily 
lessened. 


What  is  meant  by  the  term  function  of  convergence? 

When  the  word  convergence  is  used  some  students  at  once 
think  of  the  bringing  to  a  focus  of  parallel  rays  of  light,  as  by 
action  of  a  convex  lens;  but  in  this  case  the  word  refers  to  the 
function  that  has  control  of  the  direction  of  the  visual  axes  of  the 
two  eyes,  so  that  they  shall  both  meet  at  the  point  of  fixation, 
which  is  at  some  finite  distance. 


What  is  the  difference  in  the  direction  of  the  line  of  sight  and  of 
the  optic  axis  of  the  eye? 

Inasmuch  as  the  fovea  centralis  does  not  lie  exactly  upon  the 
optic  axis  it  follows  that  the  optic  axis  and  the  visual  axis,  which 
joins  the  fovea  with  the  point  looked  at,  do  not  coincide.  The  angle 
formed  at  the  nodal  point  where  the  optic  and  visual  axes  cross 
has  been  termed  the  angle  alpha,  or  angle  gamma.  Its  size  is 
variable,  in  emmetropia  usually  not  more  than  five  degrees, 
increasing  in  hypermetropia  and  decreasing  in  myopia. 


What  is  the  fundamental  difference  between  the  two  leading 
theories  of  accommodation? 

According  to  the  Helmholtz  theory  the  contraction  of  the 
ciliary  muscle  causes  a  relaxation  of  the  capsule  of  the  crystalline 
lens  and  allows  it  to  assume  a  greater  convexity  through  its 
natural  desire  to  become  so.  According  to  the  Tscherning  theory 
the  contraction  of  the  ciliary  muscle  flattens  the  periphery  of  the 
crystalline  and  causes  it  to  become  more  bulging  at  the  center. 
Under  either  condition  there  is  an  increase  in  the  dioptric  power 
of  the  lens. 


Physiological  Optics  261 

What  is  the  total  length  of  the  human  eye  and  the  dioptric  value 
when  in  a  static  condition? 

Approximately  24  mm.  and  58  D.  respectively. 


What  is  meant  by  the  term  visual  acuity? 

Visual  acuity  has  reference  to  the  image  formed  on  the  retina 
and  thence  transferred  to  the  brain.  It  is  the  sharpness  of  sight 
and  is  determined  at  a  distance  of  twenty  feet  or  more  with  accom- 
modation at  rest,  and  depends  upon  the  smallest  retinal  image, 
the  form  of  which  can  be  distinguished  by  the  brain.  It  is  ex- 
pressed by  a  fraction,  the  numerator  of  which  is  the  distance  of  the 
letters  and  the  denominator  the  size  letters  that  can  be  named. 
Visual  acuity  equals  20/20  means  that  the  letters  are  20  feet  away 
and  the  patient  can  read  the  No.  20  line. 


With  eyes  in  the  primary  position,  ivhat  prism  is  needed  to 
produce  binocidar  vision  for  a  small  object  at  a  distance  of  one  meter 
from  the  eye? 

If  we  assume  the  pupillary  distance  to  be  60  mm.  then  the 
visual  lines  will  be  the  same  distance  apart.  At  a  distance  of  one 
meter  a  prism  of  one  degree  will  show  a  displacing  power  of  10 
mm.;  therefore,  to  overcome  the  separation  of  60  mm.  at  one 
meter  distance  a  prism  of  6°  would  be  required,  or  a  3°  prism  over 
each  eye. 

What  is  the  relation  betiveen  diopters  of  accommodation  and 
meter  angles  of  convergence? 

There  is  a  close  and  constant  relation  between  the  two.  At 
a  distance  of  one  meter  there  is  one  diopter  of  accommodation 
and  one  meter  angle  of  convergence,  and  for  all  distances  the 
same  proportion  should  hold  good  — that  is,  one  meter  angle  of 
convergence  for  each  diopter  of  accommodation. 


How  can  it  be  proved  that  the  human  eye  is  not  achromatic? 

It  is  not  possible  for  red  and  violet  rays  (from  the  two  ends 
of  the  spectrum)  to  be  focused  on  the  retina  at  the  same  time. 


262  State  Board  Examinations 

But  these  colors  possess  little  luminosity  as  compared  with  yellow, 
on  which  vision  chiefly  depends,  and  hence  the  fact  that  they  are 
out  of  focus  at  the  retina  is  not  of  great  importance,  nor  does 
chromatism  manifest  itself  in  ordinary  vision  in  approximately 
normal  eyes.  Its  effects  are  more  noticeable  in  ametropes,  but 
its  existence  in  any  eye  can  be  proved  by  looking  at  a  light  through 
a  cobalt-blue  glass,  which  blocks  the  central  part  of  the  spectrum 
and  allows  mainly  the  red  and  blue  light  to  pass  through  it,  the 
two  extremes  of  the  spectrum.  The  patient  may  see  a  red  center 
with  a  blue  border,  or  a  blue  center  with  a  red  border,  depending 
on  which  color  focuses  nearest  the  retina. 


What  causes  the  amplitude  of  accommodation  to  decrease? 

Principally  due  to  loss  of  elasticity  or  increase  in  firmness 
of  the  crystalline  lens,  with  perhaps  some  loss  in  contractibility 
of  the  ciliary  muscle,  which  conditions  are  the  natural  accom- 
paniments of  age. 

What  is  meant  by  positive  and  negative  convergence? 

Positive  convergence  is  the  turning  of  the  eyes  inward  from 
parallelism,  as  in  the  act  of  convergence,  and  negative  con- 
vergence is  turning  the  eyes  outward  from  parallelism,  as  in  the 
act  of  divergence. 

In  what  units  of  measurement  is  the  amplitude  of  convergence 
expressed,  and  describe  the  unit? 

In  meter  angles,  the  unit  of  which  is  the  angle  formed  by 
the  \'isual  lines  of  the  two  eyes  meeting  at  a  point  one  meter  away. 


What  is  meant  by  the  static  refraction  of  the  eye? 

The  action  of  the  refracting  media  of  the  eye  on  light  unin- 
fluenced by  the  accommodation. 


What  is  meant  by  the  term  dynamic  refraction  of  the  eye? 

The  action  of  the  refracting  media  of  the  eye  augmented 
by  the  power  of  accommodation. 


Physiological  Optics  •  263 

Describe  two  ways  of  getting  the  amplitude  of  the  accommodation. 

The  usual  way  is  by  means  of  the  small  test  types  and  noting 
the  closest  point  at  which  they  can  be  read. 

Or  a  card  may  be  used  in  which  two  small  holes  are  pricked 
by  a  pin,  the  distance  between  which  must  be  less  than  the 
diameter  of  the  pupil.  The  card  is  held  close  in  front  of  the  eye 
and  a  small  needle  viewed  through  the  pinholes.  When  the 
needle  is  brought  too  close  it  appears  blurred  and  double.  The 
closest  point  at  which  it  remains  clear  and  single  represents 
the  amplitude  of  accommodation. 


By  what  test  may  the  effect  of  a  refractive  error  in  the  eye  be 
so  cut  down  that  vision  will  be  improved,  and  ivhat  is  the  explanation 
of  its  action? 

By  the  pinhole  test,  which  cuts  off  so  many  rays  and  nullifies 
the  refractive  power  of  the  eye,  allowing  the  image  to  be  formed 
by  the  action  of  the  pinhole  alone,  through  which  a  ray  from  each 
point  of  the  object  passes,  and  as  the  rays  pass  they  cross  and 
form  an  inverted  image. 

What  is  the  nature  of  the  retinal  image  as  to  exactness  of  focus 
in  emmetropia,  in  hypermetropia,  in  myopia  and  in  astigmatism? 

In  emmetropia  the  retinal  image  is  ideally  perfect.  In  hyper- 
metropia, if  not  of  too  high  a  degree,  it  is  approximately  distinct, 
being  made  so  by  the  accommodation;  if  the  accommodation  is 
not  used  the  image  would  be  blurred.  In  myopia  it  is  indis- 
tinct except  when  the  object  is  placed  at  the  far  point  of  the 
eye.  In  astigmatism  the  retinal  image  is  in  the  shape  of  a  line 
instead  of  a  point,  but  in  low  degrees  of  hypermetropic  astigma- 
tism the  ciliary  muscle  is  usually  able  to  make  vision  clear. 


When  the  eyes  are  first  fixed  on  an  object  at  close  range  and 
then  on  some  object  further  away  what  ocular  changes  occur? 

The  ciliary  muscles  relax  so  as  to  cause  the  crystalline  to 
become  less  convex  and  thus  adapt  the  eye  for  distant  vision; 
there  is  also  a  lessening  of  convergence  so  as  to  allow  the  visual 
axes  to  meet  at  the  greater  distance  desired. 


264  Slate  Board  Examinations 

When  the  far  point  and  near  point  are  both  positive  or  real 
what  is  the  space  between  them  called? 

The  range  of  accommodation. 


With  a  -\-  1  D.  lens  placed  in  front  of  a  certain  eye  the  near 
point  is  at  20  inches.  The  test  shon's  that  the  static  refraction  of  the 
eye  is  2.50  D.  hypermetropic.  What  is  the  amplitude  of  accommoda- 
tion? 

If  the  near  point  is  located  at  20  inches  by  the  aid  of  a  +  1 
D.  lens  then  the  unassisted  eye  would  show  a  near  point  of  40 
inches,  which  is  equivalent  to  1  D.  of  accommodation. 

However,  as  the  2.50  D.  of  hypermetropia  must  first  be 
neutralized  by  the  accommodation  before  near  vision  is  at- 
tempted, the  amplitude  of  accommodation  must  be  3.50  D. 


What  is  the  size  of  the  object  5  meters  away  that  forms  on  the 
retina  of  a  hypermetrope  of  3  D.  an  image  5  mm.  in  size? 

The  size  of  the  retinal  image  bears  the  same  relation  to 
the  size  of  the  object  as  the  distance  from  the  nodal  point  to  the 
retina  bears  to  the  distance  from  the  nodal  point  to  the  object. 
In  the  emmetropic  eye  the  distance  between  the  nodal  point 
and  the  retina  is  estimated  at  15  mm.  But  in  a  hypermetrope 
of  3  D.,  as  in  this  case,  this  distance  is  reduced  to  14  mm. 

Then  we  have  the  following  proportion :  the  size  of  the  object 
is  to  the  size  of  the  image  as  the  distance  of  the  object  is  to  the 
distance  of  the  image.     Substituting  the  figures: 
X  :  5  mm.  ::  5,000  mm.  :  14  mm. 
14  X  =  25,000  mm. 
X  =     1,785  mm. 
which  is  the  size  of  the  object. 


How  does  the  function  of  the  eye  differ  in  dynamic  and  static 
refraction? 

Static  refraction  with  the  fixation  at  20  feet  or  more  is 
considered  a  passive  condition,  while  dynamic  refraction  with 
the  fixation  at  the  reading  or  working  distance  is  an  active 
condition  with  the  ciliary  muscle  at  work. 


Physiological  Optics  265 

How  many  diopters  of  accommodation  are  required  in  an 
emmetropic  eye  to  see  clearly  an  object  at  20  feet? 

In  the  practice  of  optometry  a  distance  of  20  feet  is  selected 
for  making  the  visual  tests,  on  the  assumption  that  rays  proceed- 
ing from  this  distance  are  practically  parallel.  But  this  is  not 
strictly  correct,  because  rays  at  this  distance  have  a  divergence 
of  1/240  of  an  inch,  and  would  require  a  +  .17  D.  (one-sixth  of  a 
diopter)  to  make  them  parallel,  or  the  use  of  an  equal  amount 
of  accommodation. 


How  do  we  measure  the  amplitude  of  accommodation,  a?id 
why  is  it  expressed  in  diopters? 

We  measure  the  amplitude  of  accommodation  by  finding 
the  position  of  the  near  point,  which  is  the  closest  possible  point 
one  can  see  with  the  strongest  elTort  of  accommodation,  and  it 
is  equivalent  to  a  convex  lens  (expressed  in  diopters)  of  such 
strength  as  will  give  to  rays  proceeding  from  this  near  point, 
a  direction  as  if  they  came  from  distance,  or  in  other  words  makes 
them  parallel. 

How  is  the  size  of  the  image  of  an  object  that  is  defined  by  the 
minimum  visual  angle  at  6  meters  distance  determined  when  the 
nodal  point  of  the  eye  is  15  mm.  in  front  of  the  retina?  What  is 
the  size  of  the  objects? 

The  size  of  the  retinal  image  of  an  object  bears  the  same 
relation  to  the  size  of  the  object  itself  as  the  distance  between 
the  nodal  point  and  the  retina  bears  to  the  distance  between 
the  nodal  point  and  the  object. 

As  the  nodal  point  in  the  emmetropic  eye  is  usually  estimated 
to  be  15  mm.  from  the  retina,  the  proportion  is  as  follows:  As 
the  distance  of  the  object  is  to  the  size  of  the  object,  so  is  15  mm. 
to  the  size  of  the  retinal  image. 

Or  in  other  words,  the  size  of  the  object  is  multiplied  by  15, 
and  the  result  divided  by  the  distance  of  the  object,  in  order  to 
find  the  size  of  the  retinal  image. 


What  is  the  difference  in   the  focusing  arrangement  of  the 
human  eye  and  the  photographer' s  camera? 


266  State  Board  Examinations 

In  the  eye  the  focusing  is  accomplished  by  an  increase  or 
decrease  in  curvature  of  the  crystalline,  while  the  retina  remains 
in  a  fixed  position  to  receive  the  image.  In  the  camera,  the 
curvature  and  position  of  the  lens  is  fixed  and  unchanging,  while 
the  screen  is  adjustable  so  that  it  can  be  moved  to  the  position 
where  it  will  receive  the  image  most  distinctly. 


If  diplopia  can  he  produced  with  a  three-degree  prism  base  in, 
what  is  the  trouble? 

When  a  prism  is  placed  before  the  eyes  base  in,  the  external 
recti  muscle  are  brought  into  action  to  prevent  diplopia;  there- 
fore, if  diplopia  is  produced,  it  must  be  because  of  deficiency  in 
power  of  these  muscles. 

What  is  diplopia  and  in  what  ivay  does  it  differ  from  hetero- 
phoria? 

Diplopia  means  double  vision.  It  is  only  a  symptom,  but 
it  is  one  that  is  self-evident  and  needs  no  test  to  discover  it. 

Heterophoria  is  a  generic  term  used  to  indicate  some  im- 
balance of  the  extra  ocular  muscles.  It  is,  however,  a  latent 
condition,  and  its  existence  is  detected  only  by  the  employment 
of  certain  tests. 

Is  the  refraction  of  the  eye  affected  by  spasm  of  the  ciliary 
muscle  and  if  so  in  what  manner? 

Spasm  of  the  ciliary  muscle  by  adding  to  the  dioptric  power 
of  the  eye  changes  its  apparent  refraction.  In  hypermetropia 
such  a  spasm  conceals  part  or  all  of  the  error,  so  that  not  sufficient 
convex  will  be  accepted  or  even  concave  lenses  may  be  called  for 
instead. 

In  emmetropia,  spasm  makes  the  eye  apparently  myopic; 
and  in  myopia  causes  too  strong  a  concave  lens  to  be  chosen. 


What  must  be  the  form  of  a  cone  of  light  entering  the  static 
myopic  eye  so  as  to  be  focused  on  the  retina?  What  must  be  the  form 
of  cone  of  light  entering  the  static  hypermetropic  eye  so  as  to  focus 
on  the  retina? 


Physiological  Optics  267 

As  the  m\opic  eye  is  adapted  for  divergent  rays,  the  apex 
of  the  cone  must  be  at  the  far  point  of  such  eye.  And  as  the 
hypermetropic  eye  is  adapted  only  for  convergent  rays,  the  apex 
of  the  cone  must  be  at  the  retina. 

In  the  first  case  the  cone  of  divergent  rays  is  a  natural 
condition  as  light  proceeds  from  close  objects;  in  the  second 
case  the  cone  of  convergent  rays  must  be  produced  artifically 
by  a  convex  lens  in  front  of  the  eye. 


Supposing  a  person  otherivise  emmetropic  had  got  a  high 
degree  of  astigmatism,  what  ivill  he  probably  complain  of  in  the  way 
he  sees  objects;  in  other  words  how  will  he,  never  having  heard  of 
astigmatism,  describe  his  visual  defects?  How  could  you  make  an 
emmetrope  see  things  as  though  he  were  astigmatic? 

This  question  is  worded  strangely  as  it  is  not  customary  to 
refer  to  an  eye  as  being  emmetropic  if  it  has  a  high  degree  of 
astigmatism. 

If  one  meridian  of  an  eye  was  emmetropic  and  the  other 
chief  meridian  was  highly  ametropic,  as  for  instance  in  simple 
myopic  astigmatism,  such  an  eye  would  see  clearly  in  one  meri- 
dian and  indistinctly  in  the  other. 

For  instance,  he  might  be  able  to  see  clearly  telegraph 
poles  and  at  the  same  time  the  telegraph  wires  might  be  indis- 
tinguishable. Or  he  might  be  able  to  see  the  hands  on  the  clock 
and  tell  the  time  of  day  at  certain  periods  of  the  24  hours  and 
not  at  others;  such  cases  having  occurred  and  been  reported 
before  astigmatism  was  understood,  as  periodical  obscuration  of 
vision. 

An  emmetrope  can  be  made  artificially  hypermetropic 
astigmatic  by  placing  a  concave  cylinder  in  front  of  his  eye,  and 
myopic  astigmatic  by  placing  a  convex  cylinder  in  front  of  his 
eye. 


//  a  person  aged  twenty  is  hypermetropic  4  D.,  how  much 
accommodation  ivoiild  be  used  when  reading  at  40  cm.  ivhile  wearing 
+  1.75  D.  sphere?  How  much  accommodative  poiver  has  he  to 
spare  and  what  glasses  ought  he  to  use? 


268  State  Board  Exami>iatio)is 

This  person  must  first  correct  his  hypermetropia  by  the  use 
of  4  D.  of  accommodation,  and  then  he  must  use  another  2.50 
D.  of  accommodation  to  see  at  40  cm.,  which  equals  6.50  D., 
but  since  he  is  wearing  +  1.75  D.  spheres,  the  effort  of  accom- 
modation would  then  be 

6.50  D.  -  1.75  D.  =  4.75  D. 

The  average  amplitude  of  accommodation  for  an  emmetropic 
eye  at  twenty  years  is  10  D.,  but  since  this  person  must  use  4  D. 
of  it  to  overcome  his  hypermetropia,  the  amount  of  accommoda- 
tion available  w'ould  be  reduced  to  6  D.  If  he  is  wearing  the 
-f  1.75  D.  spheres  mentioned,  this  would  be  increased  to  7.75  D. 

As  to  what  glasses  he  should  wear,  this  is  a  question  that 
cannot  be  answered  offhand.  Ordinarily,  it  is  not  wise  to  correct 
more  than  the  manifest  error  in  any  particular  case,  and  this  is 
a  variable  quantity.  We  presume  that  the  +  1.75  D.  spheres 
he  is  wearing  represent  the  manifest  hypermetropia  and  unless 
there  are  some  special  symptoms  we  would  not  consider  a  change. 
If,  however,  there  were  urgent  symptoms  calling  for  relief, 
then  we  would  increase  the  lenses  even  to  the  extent  of  slight 
fogging. 

Describe  the  crystalline  lens  from  an  optical  point  of  view 
omitting  all  reference  to  its  minute  anatomy.  What  would  be  the 
optical  effect  of  removing  the  crystalline  lens  altogether? 

The  crystalline  lens  is  a  bi-convex  lens,  about  8  mm.  wide 
and  3.6  mm.  thick.  The  nucleus  has  a  higher  index  of  refraction 
than  the  cortex,  and  hence  the  crystalline  may  be  regarded  as  a 
biconvex  lens  of  high  power  enclosed  between  two  convexo- 
concave  lenses  of  lower  power,  and  as  a  result  of  this  construction, 
the  refractive  power  of  the  lens  is  greater,  the  alteration  in 
curvature  in  the  act  of  accommodation  is  made  possible  and 
spherical  aberration  is  reduced. 

The  radius  of  curvature  of  the  anterior  surface  of  the 
crystalline  is  about  10  mm.  and  of  the  posterior  surface  6  mm. 

The  index  of  refration  of  the  crystalline  is  about  1.44,  but  on 
account  of  the  media  on  both  sides  of  it  having  an  index  of  1.33, 
the  relative  index  of  refraction  of  the  crystalline  lens  is  expressed 
by 


Physiological  Optics  269 

Its  refracti\e  power  is  from  15  D.  to  20  D. 

The  removal  of  the  crystalline  makes  the  eye  hypermetropic 
to  the  extent  of  only  10  D.,  which  is  not  as  much  as  indicated  by 
the  power  of  the  crystalline  lens  in  the  eye,  where  its  effect  is 
lessened  by  being  in  contact  with  media  approximating  its  own 
index  of  refraction. 

What  do  you  understand  by  the  terms  "amplitude  of  accommo- 
dation" and  "range  of  accommodation?"  Illustrate  these  terms  in 
the  case  of  an  emmetrope  aged  20,  a  myope  of  3  D.  aged  20  and  a 
hypermetrope  of  3  D.  of  the  same  age.  Where  would  the  near  point 
he  situated  in  each  case? 

The  amplitude  of  accommodation  in  all  the  cases  mentioned 
at  20  years  of  age  is  10  D.,  but  the  positive  refracting  power  and 
the  near  point  vary  in  each  case. 

In  emmetropia  the  positive  refracting  power  is  identical  with 
the  amplitude  of  accommodation  and  the  near  point  is  4  inches. 

In  a  hypermetrope  of  3  D.  the  positive  refracting  power  is 
reduced  to  7  D.  and  the  near  point  recedes  to  S}4  inches. 

In  a  myope  of  3  D.  the  positive  refracting  power  is  increased 
to  13  D.  and  the  near  point  approaches  to  3  inches. 


hi  the  application  of  the  laws  of  conjugate  foci  to  the  human 
eye,  what  two  poitits  are  conjugate? 

One  conjugate  focus  is  on  the  retina  where  the  distinct  image 
must  be  formed.  The  other  conjugate  focus  will  be  the  object 
which  emits  the  rays  that  go  to  form  the  retinal  image. 

Or  we  may  say  that  the  far  point  and  the  retina  are  conjugate 
to  each  other. 

The  standard  position  of  the  retina  is  at  the  posterior  princi- 
pal focus  of  the  refracting  system  of  the  eye,  which  is  the  focus 
for  parallel  rays  proceeding  from  infinity. 

In  emmetropia  the  retina  and  infinity  are  at  conjugate  foci. 

In  myopia  the  retina  lies  beyond  the  principal  focus;  and  in 
hypermetropia  it  lies  in  front  of  it. 

When  the  retina  is  situated  beyond  the  principal  focus  as  in 
myopia,  the  emerging  rays  will  be  convergent  and  focus  at  its 
far  point,  which  is  then  conjugate  to  the  retina,  these  conjugate 
foci  being  on  opposite  sides  of  the  refracting  system  and  the  image 
is  negative. 


Anatomy  of  Eye 

Name  the  intrinsic  and  extrinsic  muscles  of  the  eye  and  the 
nerves  supplying  innervations  to  each. 

The  intrinsic  muscles  of  the  eye  are : 

{a)  Ciliary  muscle,  supplied  by  the  third  cranial,  or  oculo- 
motor nerve. 

{h)  The  muscles  of  the  iris,  of  which  the  sphincter  is  supplied 
by  the  third  cranial  nerve  and  the  dilator  by  the  sympathetic. 

The  extrinsic  muscles  are:  External  rectus,  supplied  by  the 
sixth  cranial  nerve;  internal  rectus,  superior  rectus,  inferior  rec- 
tus, inferior  oblique,  supplied  by  third  cranial  nerve;  superior 
oblique,  supplied  by  fourth  cranial  nerve. 


Name  the  hones  of  the  orbit. 

Frontal,  sphenoid,  ethmoid,  superior  maxillary,  palate,  malar 
and  lachrymal  bones. 

Describe  the  iris  and  name  its  functions.  Name  the  two  muscles 
which  control  its  movements.    Name  the  nerve  supply  of  each. 

The  iris  is  the  terminal  portion  of  the  choroid,  and  is  sus- 
pended in  the  aqueous  humor  in  front  of  the  crystalline  lens.  Its 
free  border  encircles  the  pupil  and  rests  on  the  anterior  surface 
of  the  capsule  of  the  lens.    The  diameter  of  the  iris  is  about  1 1  mm. 

Its  vascular  stroma  layer  is  composed  of  bundles  of  loose 
connective  tissue  and  contains  blood-vessels,  nerves,  lymph 
spaces,  nucleated  cells  with  pigment  and  the  muscles  of  the  iris. 

The  two  muscles  are  the  sphincter,  which  is  a  flat  band  1  mm. 
in  width,  lying  near  the  pupillary  margin,  and  the  dilator,  whose 
fibres  are  arranged  meridionally,  extending  from  the  ciliary  mar- 
gin of  the  iris  to  the  pupil.  Both  muscles  are  involuntary.  The 
former  is  supplied  by  the  third  nerve  and  the  latter  by  the  sym- 
pathetic nerve. 

270 


Anatomy  of  Eye  271 

The  iris  is  a  diaphragm,  changing  the  size  of  the  pupil  so  as 
to  regulate  the  quantity  of  light  entering  the  eye,  the  movements 
being  made  unconsciously.  These  movements  are  induced  reflexly, 
as  by  light,  and  directly,  as  by  the  accommodation. 


Describe  the  crystalline  lens  and  name  and  describe  its  functions. 

This  is  a  transparent  lenticular  body,  classed  as  biconvex, 
(the  posterior  surface  showing  the  greatest  convexity),  resting  in 
a  depression  in  the  anterior  surface  of  the  vitreous  humor  and 
supported  by  the  suspensory  ligament,  or  zone  of  Zinn.  Early 
in  life  the  lens  substance  is  soft  and  of  the  same  consistence 
throughout,  but  gradually  the  central  portion  hardens  and  in 
advanced  age  forms  the  nucleus.  This  hardening  results  in  loss  of 
elasticity  and  is  made  manifest  by  impaired  accommodation. 
The  lens  substance  is  enclosed  within  an  elastic  strong  membrane, 
called  its  capsule.  The  lens  measures  about  10  mm.  transversely 
and  4  mm.  in  thickness. 

The  substance  of  the  lens  is  composed  of  layers  of  elongated 
cells,  called  the  lens  fibers,  which  are  united  by  a  cement  sub- 
stance. 

The  function  of  the  crystalline  lens  is  to  increase  and  de- 
crease in  convexity  and  thus  provide  for  focusing  upon  the  retina 
the  rays  of  light  proceeding  from  objects  situated  at  different 
distances  within  infinity.  During  the  act  of  accommodation  the 
lens  becomes  more  convex,  especially  upon  its  anterior  surface. 
This  increase  in  convexity  is  brought  about  by  the  action  of  the 
ciliary  muscle  acting  upon  the  suspensory  ligament. 


Describe  the  anterior  chamber  of  the  eye. 

The  cavity  in  the  anterior  portion  of  the  eye  occupied  by  the 
aqueous  humor  is  divided  by  the  iris,  which  stretches  across  it 
from  side  to  side,  into  two  portions,  called  the  anterior  and 
posterior  chambers.  The  anterior  chamber  is,  therefore,  that 
portion  of  the  aqueous  cavity  lying  in  front  of  the  iris  and  is 
bounded  anteriorly  by  the  cornea. 


Which  is  the  longest  diameter  of  the  eyeball?    Why? 


272  State  Board  Examinations 

The  anlerio-posterior  diameter  is  the  longest  because  of  the 
projection  of  the  cornea. 

In  high  hypernietropia,  it  is  conceivable  that  this  diameter 
may  be  shorter. 

Give  the  location  of  the  lachrymal  gland.  Describe  briefly  the 
lachrymal  duct. 

The  lachrymal  gland  is  a  compound  racemose  gland  of  the 
size  and  shape  of  an  almond  and  is  lodged  in  a  depression  at  the 
upper  and  outer  portion  of  the  orbit.  Its  concave  under  surface 
rests  upon  the  globe  of  the  eye,  with  the  conjunctiva,  superior 
and  external  recti  muscles  intervening.  It  is  held  in  contact  with 
the  orbital  periosteum  by  a  few  fibrous  bands.  Connected  with 
the  gland  there  are  a  number  of  ducts,  from  eight  to  twelve,  which 
open  by  minute  orifices  in  a  row  on  the  upper  and  outer  part  of  the 
conjunctival  reflection. 

What  is  probably  meant  by  the  latter  part  of  the  question  is 
a  description  of  the  nasal  duct.  This  is  a  membranous  canal  about 
3/4  of  an  inch  long,  extending  from  the  termination  of  the  lach- 
rymal sac  through  the  osseous  nasal  duct  to  the  inferior  meatus  of 
the  nose,  passing  in  a  direction  downward,  backward,  and  out- 
ward, its  diameter  being  narrowest  at  its  middle.  Externally  it  is 
composed  of  fibro-areolar  tissue  and  internally  of  mucous  mem- 
brane, continuous  with  that  of  the  nose  and  lachrymal  sac. 


Name  the  humors  and  the  refracting  media  of  the  eye. 

The  humors  from  before  backward  are  the  aqueous  humor, 
crystalline  lens,  and  vitreous  humor,  which  together  with  the 
cornea,  form  the  refracting  media  of  the  eye. 


How  many  muscles  are  there  in  each  orbit?    Give  their  names. 

Answered  above,  to  which,  however,  may  be  added  the 
levator  palpebrae  superioris,  which  arises  from  the  lesser  wing  of 
the  sphenoid  bone  and  passes  forward  to  be  inserted  into  the 
upper  border  of  the  superior  tarsal  cartilage  and  the  skin. 

What  are  the  principal  blood-vessels  of  the  eye? 


Anatomy  of  Eye  273 

The  ophthalmic  artery  enters  the  orbit  by  the  optic  foramen 
and  gives  ofif  the  following  branches: 

Lachrymal,  supraorbital,  superior  and  inferior  palpebral, 
nasal,  long,  short  and  anterior  ciliary,  arteria  centralis  retinae 
and  infraorbital. 

Name  the  nerves  of  the  eyeball. 

Optic  nerve,  the  special  nerve  of  sight.  The  motor  nerves  are 
the  third,  fourth  and  sixth  cranial.  The  ophthalmic  division  of  the 
fifth  cranial  nerve  supplies  general  sensation.  The  sympathetic. 
The  long  and  short  ciliary.     Lachrymal,  frontal  and  orbital. 


What  are  the  folds  of  the  conjunctiva  called? 

The  folds  formed  by  the  passage  of  the  conjunctiva  from 
the  lids  to  the  eyeballs  are  called  the  superior  and  inferior  pal- 
pebral folds,  the  former  being  the  deeper.  The  word  fornix  is  also 
used. 

What  are  the  appendages  of  the  eye? 

The  appendages  of  the  eye  are  the  eyebrows,  or  supercilia ; 
the  eyelids,  or  palpebrae,  with  their  lashes;  the  mucous  membrane, 
or  conjunctiva,  and  the  lachrymal  apparatus,  consisting  of  the 
lachrymal  gland,  with  its  ducts,  the  canaliculi,  the  lachrymal  sac 
and  the  nasal  duct. 

Describe  the  posterior  chamber  of  the  eye. 

This  term  may  have  two  meanings.  It  is  possible  that  the 
examiners  may  have  had  reference  to  the  vitreous  chamber,  which 
lies  behind  the  crystalline  lens  and  in  front  of  the  retina  and  is 
filled  with  a  jelly-like  substance,  which  not  only  allows  the  light 
to  pass  freely  but  also  gives  form  to  the  eye. 

The  term  posterior  chamber,  or  more  properly,  posterior 
aqueous  chamber,  is  also  given  to  that  part  of  the  aqueous  cham- 
ber which  lies  behind  the  iris  and  in  front  of  the  crystalline  lens. 
The  posterior  chamber  is  only  a  narrow  chink  between  the 
peripheral  portion  of  the  iris,  the  suspensory  ligament  and  the 
ciliary  processes,  and  is  filled  with  aqueous  humor. 


274  State  Board  Examinations 

Describe  the  mechanism  of  the  contraction  and  expansioyi  of 
the  pupil  of  the  eye. 

The  pupil,  being  simply  an  aperture  in  the  iris,  its  mechan- 
ism is  supplied  by  the  muscles  of  the  latter,  which  consists  of  two 
sets  of  fibers. 

The  sphincter  of  the  pupil,  which  is  a  narrow  band  of  circu- 
lar muscular  fibers,  surrounding  the  pupil  on  its  posterior  surface 
5  mm.  wide  and  supplied  by  the  third  nerve  through  the  ophthal- 
mic ganglion. 

The  dilator  of  the  pupil,  which  consists  of  radiating  muscular 
fibers  converging  from  the  circumference  of  the  iris  toward  the 
pupillary  margin,  where  they  blend  with  the  circular  fibers  and  is 
supplied  by  sympathetic  fibers  from  the  ophthalmic  ganglion. 

The  pupil  contracts  and  dilates  automatically  on  exposure 
to  or  protection  from  light,  the  greater  part  of  these  movements 
being  due  to  the  action  of  the  sphincter  muscle,  which  is  the 
stronger  of  the  two. 

What  is  the  canal  of  Schlemm  and  where  is  it  located? 

This  canal,  also  called  the  circulus  venosus  ciliaris,  is  a  small 
channel  running  completely  around  the  eye  at  the  sclero-corneal 
juncture.  Its  outer  walls  are  dense,  while  the  inner  are  com- 
posed of  spongy,  reticulated  tissue,  apparently  continuous  with 
the  inner  scleral  process  and  closely  united  with  the  posterior 
limiting  membrane  of  the  cornea  and  with  the  pectinate  liga- 
ment of  the  iris,  and  the  meridonal  fibers  of  the  ciliary  muscle. 

The  character  of  the  canal  of  Schlemm,  whether  venous  or 
lymphatic,  was  long  a  subject  of  controversy,  but  it  is  now  re- 
garded as  a  venous  sinus,  which,  through  the  spaces  of  Fontana, 
stands  in  close  relation  to  the  anterior  chamber  on  one  hand  and 
communicates  directly  with  the  anterior  ciliary  veins  on  the  other. 
Usually  the  canal  of  Schlemm  contains  but  little  blood,  because 
it  is  only  a  reserve  reservoir  for  the  storage  of  blood  when  tem- 
porarily retarded  in  its  escape  through  the  anterior  ciliary  veins. 
In  order  to  maintain  normal  conditions  of  intraocular  tension,  the 
aqueous  humor  is  constantly  passing  through  the  space  of  Fon- 
tana into  the  canal  of  Schlemm  and  thence  into  the  communicat- 
ing veins. 


A  natomy  of  Eye  275 

What  kind  of  a  membrane  is  the  conjunctiva  and  where  is  it 
located? 

The  conjunctiva  is  a  mucous  membrane  lining  the  lids  and 
covering  the  anterior  surface  of  the  eyeball  and,  therefore,  it  is 
appropriately  divided  into  the  palpebral  and  ocular  conjunctiva. 
The  annular  fold  which  marks  the  limit  of  the  conjunctival  sac 
is  known  as  the  fornix,  which  permits  of  free  motion  of  the  ball 
in  all  directions. 

The  ocular  conjunctiva  is  smooth  and  glistening,  while  the 
tarsal  conjunctiva  shows  a  peculiar  velvety  appearance.  The 
conjunctiva  in  many  places  is  loosely  attached  and  elastic,  allow- 
ing it  to  be  moved  readily  to  and  fro  and  at  the  same  time  affords 
an  opportunity  for  the  accumulation  of  extravasated  fluids. 


What  is  the  function  of  the  lachrymal  gland  and  where  is  it 
located? 

The  lachrymal  gland  is  located  in  a  depression  in  the  roof 
of  the  orbit  at  its  upper  and  outer  portion.  Its  function  is  to 
secrete  a  fluid  called  the  tears,  which  keep  the  eye  moist  and  lubri- 
cate it.  Under  the  disturbing  influence  of  emotion,  a  foreign 
body  in  the  eye,  and  inflammation,  an  excessive  secretion  takes 
place,  causing  a  running  of  the  nose  and  an  overflow  on  the 
cheeks. 

How  is  the  crystalline  lens  held  in  position? 

The  position  of  the  crystalline  lens  is  maintained  by  means 
of  a  series  of  delicate  bands  which  pass  from  the  vicinity  of  the 
ora  serrata  over  the  ciliary  processes,  to  be  attached  to  the 
periphery  of  the  lens;  these  fibers  constituting  the  suspensory 
ligament  or  zone  of  Zinn.  This  structure  is  of  great  importance, 
not  only  for  the  support  of  the  lens,  but  also  in  effecting  changes 
in  the  curvature  of  the  lens  in  the  act  of  accommodation.  The 
suspensory  ligament  is  a  delicate  annular  band  about  6  mm.  in 
width,  which  blends  with  the  periphery  of  the  lens  on  one  hand 
and  with  the  hyaloid  membrane  in  the  vicinity  of  the  ora  serrata 
on  the  other. 

The  zone  of  Zinn  is  not  a  continuous  membrane  but  a  series 
of  interlacing  bands  or  fibers,  which  are  divided  into  chief  and 


276  State  Board  Examinations 

accessory.  The  chief  zonular  fibers  constitute  the  principal  union 
between  the  lens  and  the  surrounding  ciliary  body,  while  the 
accessory  fibers  comprise  numerous  shorter  bands,  which  act  as 
bracers  and  binders  to  the  chief  fibers,  and  hence  are  important 
additions  to  the  strength  of  the  suspensory  ligament. 


What  are  the  characteristics  of  the  choroid? 

This  is  the  middle  coat  of  the  eyeball  and  is  essentially  a 
sheet  of  vascular  connective  tissue.  It  extends  from  the  optic 
nerve  entrance  to  the  ora  serrata,  closely  united  to  the  retina, 
whose  nutrition  it  furnishes.  Although  lining  the  sclerotic,  its 
connection  with  the  outer  coat  is  not  so  firm. 

The  most  conspicuous  of  the  large  blood  channels  are  the 
four  venous  trunks  the  venae  vorticosae,  which  pierce  the  choroid 
at  its  equator  at  equidistant  points,  toward  which  the  smaller 
veins  converge.  The  choroid  is  dark  in  color,  fragile  and  easily 
torn. 

What  are  the  angles  of  the  eyelids  called? 

They  are  called  outer  and  inner  canthi,  from  the  Latin  word 
meaning  corners.    The  singular  noun  is  canthiis. 


How  is  the  eye  protected  from  external  injury? 

The  eyeball  itself  is  protected  from  injury  by  being  deeply 
placed  in  the  orbit,  the  edges  of  which  are  dense  and  strong, 
particularly  the  upper  one,  which  overhangs  the  eye  and  is 
capable  of  shielding  it  from  a  powerful  blow,  as  is  shown  in  the 
case  of  a  "black  eye,"  where  the  blackness  is  not  in  the  eye  but 
in  the  surrounding  soft  tissues,  which  are  swollen  and  inflamed 
and  filled  with  blood,  while  the  eye  itself  peeps  through  them 
quite  unharmed.  If  the  force  of  the  injury  is  from  below  the  eye 
is  not  so  well  protected. 

The  contents  of  the  eyeball  are  protected  by  the  sclerotic, 
which  is  a  dense,  strong,  fibrous  coat;  and,  in  addition,  by  reflex 
and  automatic  action,  when  any  foreign  body  approaches  the 
eye  the  muscles  instinctively  contract  and  the  eye  is  immediately 
closed. 


A  natomy  of  Eye  277 

Name  the  humors  of  the  eye  and  state  in  what  respect  they 
differ. 

The  humors  of  the  eye  from  before  backwards  are  the 
aqueous,  crystalHne  and  vitreous. 

The  aqueous  humor  has  the  consistency  of  water,  with  an 
index  of  refraction  of  1.333. 

The  vitreous  humor  is  thicker,  of  jelly-Hke  nature,  resembhng 
the  white  of  a  fresh  egg,  with  an  index  of  refraction  about  the 
same  as  the  aqueous. 

The  crystalHne  lens  is  of  still  greater  consistency  than  the 
vitreous,  with  the  nucleus  denser  than  the  cortex.  The  index  of 
refraction  of  the  crystalline  as  a  whole  is  about  1.44. 

They  differ  in  their  density  and  refractive  power,  the 
crystalline  leading  in  each  particular. 


Describe  the  eyelids. 

The  lids  from  without  inwards  are  composed  of  the  following 
structures: 

Skin,  thin  layer  of  connective  tissue,  fibers  of  the  orbicularis 
palpebrarum,  which  closes  the  lids,  small  plates  of  cartilage,  known 
as  the  tarsal  cartilages  and  composed  of  dense  fibrous  tissue,  and 
giving  form  and  support  to  the  lids.  Meibomian  glands,  whose  oily 
secretion  prevents  adhesion  of  the  lids  and  mucous  membrane 
known  as  the  conjunctiva. 

In  addition  to  the  orbicularis  muscle,  there  is  the  levator 
palpebrae  superioris,  which  raises  the  upper  lid  and  opens  the  eye. 

The  upper  lid  is  much  the  largest  and  thus  gives  better 
protection  to  the  eyeball.  The  opening  between  lids  is  the 
palpebral  fissure  or  commissure,  and  the  angles  formed  by  the 
lids  are  the  outer  and  inner  canthi. 


Name  and  briefly  describe  the  coats  of  the  eyeball. 

The  external  coat  is  the  sclerotic,  a  tough  fibrous  coat  for 
protection. 

The  middle  coat  is  the  choroid,  the  vascular  and  pigmen- 
tary coat. 

The  internal  coat  is  the  retina,  the  nervous  coat  on  which 
the  images  are  formed. 


278  State  Board  Examinations 

Describe  the  cornea.  Give  its  radius  of  curvature  and  its 
refractive  index. 

The  cornea  is  the  transparent  anterior  portion  of  the  external 
coat.     It  is  composed  of  five  layers: 

1.  Epithelium. 

2.  Anterior  limiting  membrane,  or  Membrane  of  Bowman. 

3.  The  proper  substance  of  the  cornea. 

4.  Posterior  limiting  membrane,  or  Membrane  of  Descemet. 

5.  Endothelium. 

Its  index  of  refraction  is  1.33,  and  its  radius  of  curvature 
7.8  mm.  to  8  mm. 

Enumerate  the  various  external  motor  muscles  of  the  eyeball, 
and  give  the  action  of  each.  What  is  meant  by  conjugate  movement 
of  the  eyes? 

The  superior,  inferior,  external  and  internal  recti,  the  actions 
of  which  are  to  turn  the  eye  up,  down,  out  and  in;  and  the 
superior  and  inferior  oblique,  which  produce  a  wheel-like  move- 
ment, the  former  rotating  down  and  out,  and  the  latter  up  and 
out. 

The  associated  movements  of  the  eyes  are  both  eyes  upward 
or  downward,  both  eyes  turn  to  right  or  to  left,  in  all  four  of 
which  the  axes  of  the  eyes  remain  parallel;  and  the  two  eyes 
turning  inward  in  the  act  of  convergence,  where  the  parallel 
condition  of  the  visual  axes  is  destroyed. 


Name  the  appendages  of  the  eye. 

The  eyebrows,  the  eyelids,  capsule  of  Tenon,  conjunctiva, 
the  extra-ocular  muscles  and  the  lachrymal  apparatus. 


What  muscles  are  supplied  by  the  third  nerve,  and  what  is  the 
possible  result  if  the  impulses  go  wrong? 

The  third  cranial  nerve  supplies  the  superior,  inferior  and 
internal  recti,  the  inferior  oblique,  the  ciliary  muscle  and  the 
circular  fibers  of  the  iris.  If  there  is  any  interference  with  its 
function,  the  action  of  one  or  more  or  all  of  these  muscles  will 
be  impaired. 


Anatomy  of  Eye  279 

What  are  the  ahdncens  muscles  of  the  eye,  and  why  so  called? 

The  external  recti  which  turn  the  eye  outwards;  the  word 
"abducens"  is  derived  from  two  Latin  words,  meaning  "to  lead 
from." 

What  is  the  nature  of  the  aqueous  humor  of  the  eye? 

It  is  a  watery  fluid  with  a  sHght  quantity  of  chloride  of 
sodium  in  solution,  and  with  an  index  of  refraction  about  the 
same  as  water.  If  lost  by  injury  or  operation,  it  is  quickly  re- 
placed. It  has  free  communication  with  the  spaces  of  Fontana, 
the  canal  of  Schlemm  and  the  lymphatics  of  the  eye. 


Describe  the  Meibomian  glands? 

These  are  the  sebaceous  glands  of  the  eyelids,  numbering 
from  30  to  40  in  the  upper  lid,  and  20  to  30  in  the  lower.  Each 
gland  has  a  duct,  these  ducts  terminating  as  minute  points 
arranged  in  a  row  along  the  margin  of  the  lid  near  its  inner 
border.  The  oily  secretion  of  these  glands  hinders  the  overflow 
of  tears  and  prevents  adhesion  of  the  lids. 


As  a  rule  which  meridian  of  the  eye  has  the  greater  curvature? 

This  question  should  read  which  meridian  of  the  cornea, 
and  the  answer  would  be  the  Aertical. 


Where  is  the  fovea  centralis  and  why  is  it  so  important? 

It  is  a  funnel  shaped  depression  near  the  center  of  the 
macula  latea.  It  is  the  region  of  most  acute  vision,  and  because 
this  acuity  of  vision  is  confined  to  such  a  small  point,  the  eye 
must  move  when  scanning  a  surface  of  any  size. 

Its  diameter  is  from  0.2  to  0.4  mm.,  and  the  retina  at  its 
bottom  is  thinner  than  at  any  other  place.  On  account  of  this 
thinness  of  the  retina  allowing  the  pigment  to  show  through, 
the  fovea  appears  as  a  dark  brown  spot. 


ophthalmoscopy 

Describe  the  indirect  method  of  ophthalmoscopy,  give  the 
character  of  the  image  seen  and  state  where  it  is  located. 

In  the  indirect  method  of  the  ophthalmoscope,  a  strong  con- 
vex lens  is  used  in  connection  with  the  instrument.  This  lens  may 
be  +  13  D.  or  +  16  D.  and  is  held  at  its  focal  distance  in  front 
of  the  eye.  The  ophthalmoscope  is  held  at  a  distance  of  12  to  15 
inches  from  the  eye,  and  the  light  is  reflected  through  the  convex 
lens  into  the  eye.  The  rays  returning  from  the  retina  of  the  eye 
under  observation  form  a  real,  inverted,  aerial  image  between  the 
lens  and  the  ophthalmoscope.  If  the  patient  is  requested  to  turn 
his  eye  in  accordance  with  the  observer's  wishes,  every  part  of 
the  fundus  may  be  brought  into  view.  This  aerial  image  may  be 
magnified  and  hence  better  seen  by  rotating  a  convex  lens  of  3 
D.  or  4  D.  into  the  sight  hole  of  the  instrument. 

The  indirect  method  gives  a  larger  field  than  the  direct,  but 
the  details  are  less  magnified,  usually  about  5  diameters  as  com- 
pared with  sixteen  diameters  in  the  direct.  The  stronger  the  con- 
densing lens,  the  larger  the  field,  but  the  smaller  the  details; 
the  weaker  the  condensing  lens,  the  smaller  the  view  of  the  fundus, 
but  the  larger  the  details. 


Name  the  various  methods  of  using  the  ophthalmoscope.  How 
do  the  images  differ?   What  are  the  advantages  of  each  method? 

There  are  two  methods  of  using  the  ophthalmoscope  —  the 
direct  and  the  indirect. 

In  the  direct  the  image  is  erect  and  magnified.  In  the  in- 
direct, inverted  and  smaller  than  in  the  direct. 

The  advantages  of  the  direct  method  are  the  greater  magni- 
fication and  the  disk  seen  in  the  erect  position. 

The  advantages  of  the  indirect  method  are  the  larger  field 
of  view,  can  be  seen  through  a  smaller  pupil  and  not  necessary  to 
get  so  close  to  objectionable  patients. 

280 


ophthalmoscopy  281 

In  what  manner  is  the  ophthalmoscope  or  mirror  used  in  cases 
of  matured  cataract,  so  as  to  determine  the  extent  of  retinal  light 
sensibility  in  support  of  a  favorable  prognosis  to  operation? 

Before  the  whole  lens  has  become  opaque  examination  with 
an  oblique  light  will  throw  a  shadow  of  the  iris  on  the  cataractous 
part  on  the  side  from  which  the  light  comes,  which  shadow  is 
absent  when  the  cataract  has  become  mature. 

If  the  retinal  sensibility  is  unimpaired,  the  perception  of  light 
is  never  lost  even  in  mature  cataract ;  hence  when  light  is  reflected 
into  the  eye  the  patient  should  be  able  to  quickly  recognize  the 
direction  in  which  it  is  moved. 


How  are  errors  of  refraction  detected  by  the  direct  method  of 
ophthalmoscopy? 

The  accommodation  of  both  optometrist  and  patient  must  be 
relaxed  and  the  former  must  wear  his  correcting  lenses  or  make 
allowance  for  his  error. 

Hypermetropia  is  detected  and  measured  by  the  strongest 
convex  lens  with  which  the  fundus  can  be  seen;  myopia  by  the 
weakest  concave  lens  that  makes  the  fundus  clear,  and  astig- 
matism by  the  difference  in  the  lenses  required  for  vertical  and 
horizontal  vessels. 


How  is  the  refraction  of  the  eye  measured  by  the  indirect  method 
of  ophthalmoscopy? 

As  the  object  lens  is  withdrawn,  if  the  disk  remains  unchanged 
in  size,  emmetropia  is  indicated;  if  it  diminishes  in  size,  hyper- 
metropia; and  if  it  increases  in  size,  myopia.  This  is  a  method  for 
detection  of  these  errors,  but  cannot  be  used  for  accurate 
measurements. 

How  is  the  examination  with  the  ophthalmoscope  made  by  the 
direct  method? 

Looking  directly  into  the  eye,  examining  patient's  right  eye, 
observer  uses  his  right  eye  and  holds  ophthalmoscope  in  his  right 
hand.  Commencing  the  examination  at  a  distance  of  at  least  ten 
or  twelve  inches  and  then  without  losing  the  reflex  approaching 


282  State  Board  Examinations 

as  close  as  possible  in  a  slow  and  easy  manner,  until  the  full 
details  of  the  fundus  are  distinctly  visible. 


How  is  the  examination  with  the  ophthalmoscope  by  the  indirect 
method? 

The  observer  does  not  have  to  get  so  close  to  his  patient, 
but  holds  the  ophthalmoscope  at  a  distance  of  twelv^e  inches.  A 
strong  convex  lens  is  required,  which  is  held  at  its  focal  distance 
in  front  of  the  eye.  The  light  is  reflected  through  the  convex  lens 
into  the  patient's  eye  and  the  slight  movements  made  that  may 
be  necessary  to  bring  the  disk  and  vessels  into  view.  The  observer 
is  supposed  to  see  a  real  inverted  image  formed  in  the  air  between 
the  lens  and  the  ophthalmoscope,  this  image  being  also  laterally 
transposed.  In  order  to  get  a  better  view  of  the  image  the 
operator  may  use  a  convex  lens  (about  4  D.)  in  the  sight  hole  of 
the  ophthalmoscope. 

Explain  how  the  ophthalmoscope  may  he  used  to  detect  and 
measure  errors  of  refraction? 

By  means  of  the  direct  method  with  the  accommodation 
of  both  patient  and  observer  at  rest,  the  strongest  convex  lens  or 
the  weakest  concave  lens  rotated  into  the  sight  hole  of  the  instru- 
ment, with  which  the  details  of  the  fundus  can  be  clearly  seen,  will 
represent  the  amount  of  hypermetropia  or  myopia  respectively. 


In  what  way  does  the  picture  of  the  retina  as  seen  by  the  direct 
method  of  ophthalmoscopy  differ  from  that  seen  with  the  indirect 
method? 

In  the  direct  method  the  image  is  erect  and  more  magnified, 
with  a  restricted  field.  In  the  indirect  method  the  image  is 
inverted,  less  magnified,  but  with  a  larger  field  of  view. 


Why  is  refracting  with  the  ophthalmoscope  apt  to  be  incorrect, 
and  when  will  it  he  the  most  reliable? 

Because  of  action  of  the  accommodation  in  patient  or  optom- 
etrist.   In  order  to  obtain  accurate  results  in  measuring  the  refrac- 


ophthalmoscopy  283 

tion  with  the  ophthalmoscope  the  accommodation  of  both  ob- 
server and  observ'ed  must  be  at  rest,  which  is  almost  an  impossi- 
bility. 

The  result  of  such  a  test  would  be  most  reliable  if  the  accom- 
modation of  both  was  under  the  influence  of  a  cyclopegic,  or  if 
both  were  past  the  presbyopic  age.  But  as  a  matter  of  fact  the 
ophthalmoscope  has  been  supplanted  by  the  retinoscope  for 
measuring  the  refraction. 


Where  are  the  images  formed  in  the  direct  and  indirect  methods 
of  the  ophthalmoscope? 

In  the  direct  method  the  image  is  virtual,  erect  and  enlarged, 
and  appears  to  be  some  distance  behind  the  eye. 

In  the  indirect  method  the  image  is  real,  inverted  and  smaller ; 
it  is  an  aerial  image  formed  between  the  convex  lens  and  the 
ophthalmoscope. 

Which  gives  the  best  view  of  the  fundus  of  the  eye,  the  direct 
method  of  ophthalmoscopy  or  the  indirect  method? 

The  direct  method  gives  an  erect  magnified  view  of  the  fun- 
dus. The  indirect  affords  an  inverted  less  magnified  view  but  with 
a  much  larger  extent  of  the  surface  of  the  fundus  visible.  On 
account  of  the  magnification  the  direct  method  is  usually  con- 
sidered the  best. 


Describe  the  optic  disk  as  seen  by  the  ophthalmoscope  when 
in  a  normal  condition.  What  peculiarities  are  sometimes  noted  in 
the  fundus  of  the  normal  eye? 

The  optic  disk  is  the  most  conspicuous  landmark  of  the 
fundus  and  is  the  head  of  the  optic  nerve.  It  is  nearly  circular  or 
slightly  oval,  with  a  diameter  of  1.5  mm.,  which  is  magnified 
fifteen  times  by  the  direct  method  of  the  ophthalmoscope.  The 
disk  projects  slightly  above  the  level  of  the  fundus  and  presents 
a  central  depression.  The  color  is  whitish  or  pinkish,  and 
presents  a  marked  contrast  with  the  red  of  the  fundus.  The 
edges  of  the  disk  should  be  clearly  defined. 

There  are  variations  in  the  color  of  the  fundus,  shape  of  the 
disk,  width  of  the  scleral  and  choroidal  rings,  distinctness  of  the 


284  State  Board  Examinations 

margins,  color  and  size  of  the  blood  vessels,  pulsation  of  retinal 
veins,  etc. 

/;/  direct  ophthalmoscopy  an  optometrist  whose  correction  is 
-\-  2  D.  sphere  combined  with  a  —  1  cylinder  axis  180°  fields  that 
ivith  naked  eye  he  can  see  the  blood  vessels  in  the  disk  in  the  horizontal 
meridian  with  a  -\-  1  D.  lens  in  the  ophthalmoscope,  but  requires 
-\-  2  D.  lens  to  see  the  blood  vessels  in  the  vertical  meridian.  Write 
a  prescription  for  the  eye  being  examined. 

An  analysis  of  this  sphero-cylinder  will  show  that  the 
optometrist  has  compound  hypermetropic  astigmatism,  his 
correction  being  +  1  D.  vertically  and  +  2  D.  horizontally.  In 
the  first  place  it  must  be  remembered  that  he  sees  the  horizontal 
blood  vessels  with  the  vertical  meridian  of  his  eye,  and  the  vertical 
blood  vessels  with  the  horizontal  meridian  of  his  eye.  Therefore, 
if  he  requires  +  1  D.  to  see  the  horizontal  vessels  that  means 
+  1  D.  for  his  vertical  meridian,  and  if  he  requires  +  2  D.  for 
the  vertical  vessels,  that  means  +  2  D.  for  his  horizontal  meridian. 

As  these  are  exactly  the  powers  required  in  each  meridian 
to  correct  his  own  astigmatism  the  refraction  of  the  patient  is 
proven  to  be  emmetropic  and  no  glasses  are  required. 


What  is  the  principal  optical  point  in  the  use  of  the  ophthalmo- 
scope by  the  direct  method? 

That  the  rays  emerging  from  the  observed  eye  may  be 
exactly  focused  upon  the  retina  of  the  observer,  and  these  emer- 
gent rays  must  be  of  such  character,  either  naturally  or  made  so 
artificially,  that  this  may  be  accomplished  with  the  accommoda- 
tion of  both  parties  at  rest. 

If  the  observer  is  emmetropic  and  the  patient  emmetropic 
also,  the  emerging  rays  will  be  parallel,  and  will  focus  on  retina 
of  observer  without  accommodative  eiTort.  If  the  patient  is 
hypermetropic  the  emerging  rays  will  be  divergent  and  a  convex 
lens  will  be  required  to  focus  them  in  observer's  eye,  presuming 
the  accommodation  of  both  to  be  passive. 

If  the  patient  is  myopic  the  emerging  rays  will  be  convergent 
and  a  concave  lens  will  be  required  for  the  observer  to  get  a 
good  view  of  the  fundus. 


ophthalmoscopy  285 

In  measuring  ametropia  by  the  ophthalmoscope ,  what  must  be 
allowed  for  and  what  function  must  be  passive? 

Any  error  of  refraction  in  the  eye  of  the  optometrist  must  be 
allowed  for  unless  he  wears  his  correcting  lenses,  and  the  accom- 
modation of  both  patient  and  observer  must  be  at  rest. 


What  is  the  main  purpose  of  the  ophthalmoscope? 

To  determine  the  transparency  of  the  refracting  media,  to 
examine  the  fundus  and  note  the  condition  of  the  optic  disk 
and  macula;  in  short  to  ascertain  the  absence  or  presence  of 
disease,  and  in  the  case  of  the  latter  its  character  and  location. 


In  the  direct  method  of  the  ophthalmoscope  the  examiner  finds 
that  with  the  naked  eye  he  can  see  the  blood  vessels  of  the  disk  in 
the  horizontal  meridian  with  a  -\-  1  D.  lens  in  the  instrument,  but 
requires  a  -\-  2  D.  lens  to  see  the  blood  vessels  in  the  vertical  meridian. 
The  error  of  refraction  in  the  examiner's  eye  is  corrected  by  -\-  2  D.  S. 
^  —  J  D.  cyl.  axis  180°;  what  is  the  correction  for  the  eye  under 
the  examination? 

In  the  estimation  of  the  refraction  of  an  astigmatic  eye  by 
the  direct  method  of  the  ophthalmoscope,  it  must  be  remembered 
that  when  looking  at  a  vertical  blood  vessel  the  observer  sees  it 
through  the  horizontal  meridian,  and  when  viewing  a  horizontal 
vessel,  through  the  vertical  meridian. 

The  wording  of  this  question  is  ambiguous,  as  for  instance, 
the  statement  "the  blood  vessels  of  the  disk  in  the  horizontal 
meridian."  We  do  not  know  if  the  framer  of  the  question  means 
the  vertical  vessels  which  must  be  seen  through  the  horizontal 
meridian  or  the  horizontal  vessels  which  would  be  seen  through 
the  vertical  meridian. 

Judging  from  the  correcting  lenses  of  the  examiner,  we  know 
his  vertical  meridian  is  hypermetropic  1  D.,  and  his  horizontal 
meridian  hypermetropic  2  D.,  and  as  he  is  making  the  examina- 
tion with  his  naked  eye,  this  error  of  refraction  must  be  allowed 
for.  If  the  "vessels  in  the  horizontal  meridian"  means  vertical 
vessels  seen  through  the  horizontal  meridian,  for  which  the 
correction  is   +   1   D.,  while  the  refraction  of  this  meridian  in 


286  State  Board  Examinations 

the  examiner's  eye  is  hypermetropic  2  D.,  we  must  assume  the 
patient  is  myopic  1  D.  in  this  meridian. 

And  from  a  like  point  of  view,  if  +  2  D.  is  the  correction  in 
the  sight  hole  of  the  instrument  for  the  vertical  meridian,  while 
the  examiner  is  hypermetropic  only  to  the  extent  of  1  D.  in  this 
meridian,  then  the  presumption  is  that  the  patient  is  also  hyper- 
metropic 1  D.  in  this  meridian. 

The  patient's  correction  for  the  two  meridians  would  be 
-  1  D.  cyl.  axis  90°  C  +  1  D.  cyl.  axis  180°  or  -  1  D.  C  +  2 
D.  cyl.  axis  180°. 

But  if  the  words  "vessels  in  horizontal  meridian"  mean 
horizontal  vessels,  then  the  +  1  D.  required  is  the  correction  for 
the  vertical  meridian.  And  as  this  +  1  D.  is  required  to  correct 
the  examiner's  hypermetropia  in  this  meridian,  we  must  assume 
the  patient's  refraction  is  emmetropic  in  this  meridian. 

And  in  like  view  of  the  case  the  +  2  D.  required  for  the 
vertical  vessels,  would  indicate  the  correction  for  the  horizontal 
meridian.  And  as  a  lens  of  like  amount  is  required  to  correct 
the  examiner's  hypermetropia  in  this  meridian,  the  inference  is 
the  patient  is  emmetropic  in  this  meridian. 

From  the  latter  interpretation  of  the  case,  we  would  have  no 
prescription  to  write,  as  the  patient  would  be  shown  to  be  emme- 
tropic. 

What  are  the  optical  principles  of  ophthalmoscopy  in  emme- 
tropia  by  the  direct  method? 

In  ophthalmoscopy  when  the  interior  of  the  eye  is  illuminated 
by  the  mirror  the  fundus  becomes  a  luminous  body  and  gives  off 
rays  of  light.  As  these  rays  pass  out  of  the  pupil  they  are  subject 
to  refraction  of  the  dioptric  media  of  the  eye,  and  can  be  used 
by  an  observing  eye  so  as  to  have  an  image  of  this  fundus  formed 
upon  its  retina.  It  was  the  theory  of  Helmholtz,  who  gave  us 
ophthalmoscopy,  to  bring  the  illuminated  fundus  of  the  observed 
eye  and  the  retina  of  the  observing  eye  in  positions  of  conjugate 
foci. 

He  reasoned  that  if  the  fundus  of  an  eye  became  the  source 
of  light,  the  rays  in  passing  out  through  the  optical  system  of 
the  eye  would  be  refracted  and  proceed  toward  the  conjugate 
focus  of  the  object  from  which  they  came.     If  now  the  eye  of 


ophthalmoscopy  287 

an  observer  could  be  placed  in  the  path  of  these  emergent  rays 
so  that  they  could  be  focused  on  its  retina,  the  fundus  from  which 
these  rays  proceeded  could  be  seen  in  all  its  details. 

In  emmetropia  the  rays  will  emerge  from  the  observed  eye 
parallel.  If  now  the  eye  of  the  observer  that  is  placed  in  the 
path  of  these  returning  rays  is  also  emmetropic  and  as  such 
adapted  for  parallel  rays,  the  retina  of  the  observed  eye  and  of 
the  observer's  eye  will  be  at  conjugate  foci,  and  an  image  of  the 
fundus  of  the  first  will  be  formed  on  the  retina  of  the  second. 
Therefore  an  emmetropic  eye  can  see  clearly  the  details  of  the 
fundus  of  another  emmetropic  eye  when  both  eyes  are  in  a  static 
condition  and  without  the  intervention  of  any  lens. 


What  are  the  optical  principles  of  ophthalmoscopy  in  myopia 
by  the  direct  method? 

In  myopia  the  rays  as  they  emerge  are  convergent  toward 
the  far  point  situated  at  some  finite  distance.  The  eye  of  the 
observer  if  emmetropic  and  as  such  adapted  for  parallel  rays, 
could  not  focus  these  convergent  rays  on  its  retina. 

In  order  to  accomplish  this,  the  rays  must  first  be  made 
parallel,  which  can  be  done  by  the  interposition  of  a  concave 
lens  of  such  strength  as  will  lessen  the  convergence  of  the  rays 
and  make  them  parallel.  The  negative  focus  of  this  lens  will 
coincide  with  the  location  of  the  far  point  and  the  amount  of 
myopia  of  the  obser\ed  eye. 

In  this  way  the  opthalmoscope  may  be  used  in  the  direct 
method  to  measure  the  degree  of  myopia.  When  the  emmetrope 
looks  into  the  eye  of  a  myope,  the  fundus  is  very  much  blurred. 
A  concave  lens  rotated  into  the  sight  hole  of  the  instrument 
clears  it  up  and  the  weakest  lens  that  afTords  the  clearest  view  of 
the  optic  disk  and  vessels  will  be  the  measure  of  the  myopia; 
such  lens  making  the  emergent  convergent  rays  parallel  and 
bringing  the  retinae  of  the  two  eyes  into  positions  of  conjugate  foci. 


What  are  the  optical  principles  of  ophthalmoscopy  in  hyperme- 
tropia  by  the  direct  method? 

In  hypermetropia  the  far  point  is  negative  and  the  rays  as 
they  emerge  from  the  observed  eye  are  divergent.     The  eye  of 


288  State  Board  Examinations 

the  observer  if  emmetropic  and  in  a  static  condition,  when  placed 
in  the  path  of  these  divergent  rays,  is  unable  to  focus  them  upon 
its  retina  until  they  have  been  rendered  parallel. 

This  can  be  accomplished  by  the  interposition  of  a  convex 
lens,  whose  focus  would  correspond  to  the  negative  focus  back 
of  the  retina.  The  two  retina?  are  then  placed  in  the  positions 
of  conjugate  foci  and  the  image  of  the  fundus  of  the  observed 
eye  is  formed  on  the  retina  of  the  observing  eye. 

A  convex  lens  is  rotated  in  the  sight  hole  of  the  instrument 
and  the  strongest  convex  lens  with  which  the  clearest  view  of 
the  fundus  can  be  obtained  will  be  the  measure  of  the  hyperme- 
tropia,  such  lens  making  the  emerging  divergent  rays  parallel 
and  bringing  the  retinae  of  the  two  eyes  into  positions  of  con- 
jugate foci. 

What  are  the  optical  principles  of  ophthalmoscopy  by  the 
indirect  method? 

The  convergent  rays  that  emerge  from  a  myopic  e\e  form 
an  inverted  image  of  the  fundus  of  such  eye  at  the  far  point, 
and  if  the  observer  places  himself  at  the  proper  distance  so  that 
his  own  far  point  coincides  with  this  image  he  will  be  able  to 
see  it  distinctly. 

In  the  indirect  method  of  the  ophthalmoscope  we  make  the 
observed  eye  artificially  myopic  by  means  of  a  strong  convex 
lens  placed  in  front  of  it.  It  is  customary  to  use  a  +  20  D. 
lens,  which  in  the  case  of  an  emmetropic  eye  would  form  an 
inverted  image  of  the  fundus  2  inches  in  front  of  the  lens,  which 
would  then  be  its  conjugate  focus. 

An  emmetropic  observer  at  the  usual  reading  distance  by  the 
aid  of  his  accommodation,  would  be  able  to  bring  his  far  point 
to  the  position  of  this  image,  which  would  then  be  pictured  on 
his  retina. 

If  the  eye  under  examination  be  myopic  the  aerial  image 
will  be  a  little  closer,  and  if  the  eye  be  hypermetropic  a  little 
farther,  than  in  emmetropia. 

Should  the  observer  be  presbyopic  and  unable  to  use  his 
accommodation,  a  convex  lens  rotated  into  the  sight  hole  of  the 
ophthalmoscope  whose  focal  length  would  coincide  with  the 
aerial  image  would  render  the  rays  coming  from  it  parallel,  so 
that  they  could  be  focused  by  the  eye  of  the  observer. 


ophthalmoscopy  289 

If  the  observer  is  hypermetropic  a  stronger  lens  will  be 
necessary;  if  myopic  a  weaker  lens  or  no  lens  at  all  if  the  myopia 
was  of  such  amount  that  its  far  point  coincided  with  the  aerial 
image. 


Retinoscopy 

Where  is  the  nodal  point  of  the  observing  eye  with  respect  to  the 
observed  fundus  located  when  the  point  of  reversal  in  skiametry  has 
been  reached? 

Conjugate  to  it. 


Describe  the  behavior  of  the  plane  and  of  the  concave  mirror  in 
skiametry. 

The  rays  of  light  proceeding  from  the  round  opening  in  the 
chimney  are  divergent,  and  after  striking  the  plane  mirror  are 
reflected  in  a  continuance  of  the  divergence,  just  as  if  they  came 
from  a  point  as  far  back  of  the  mirror  as  the  chimney  is  in  front 
of  it;  hence,  the  shadow  moves  with  in  hypermetropia  and  emme- 
tropia,  and  against  in  myopia. 

With  the  concave  mirror,  on  the  other  hand,  the  rays  which 
leave  the  source  of  light  as  divergent,  are  reflected  from  the 
mirror  convergently  and  brought  to  a  focus  and  cross  before 
entering  the  observed  eye,  and  consequently  the  shadow  moves 
against  in  emmetropia  and  hypermetropia,  and  with  in  myopia. 

In  both  cases  we  proceed  to  estimate  the  refraction  in  the 
same  way,  that  is,  by  neutralization  by  the  indicated  lenses. 


What  is  indicated  by  the  form  of  the  shadow  in  skiametry? 
by  the  direction  of  the  shadow?  by  the  speed  of  the  shadow? 

1.  The  form  of  the  shadow  indicates  the  character  of  the 
error,  whether  astigmatic  or  spherical.  If  the  shadow  is  curved 
or  crescent-shaped  at  its  edge,  the  indications  point  to  simple 
myopia  or  hypermetropia.  If  the  edge  is  straight  or  shows  a 
banded  appearance,  the  indications  point  to  astigmatism. 

2.  The  recognition  of  the  direction  of  the  shadow  is  a  most 
important  point,  as  it  indicates  the  character  of  the  refraction. 

Using  the  plane  mirror,  if  the  direction  is  "with,"  it  may  be 
emmetropia  or  myopia  less  than  1  D.,  but  we  usually  suspect 

290 


Retinoscopy  291 

hypermetropia,  which  is  proven  to  be  present  if  the  movement 
continues  "with"  after  a  +  1  D.  lens  is  used  to  neutralize  the  one 
meter  distance.  If  the  direction  is  "opposite,"  the  indications 
are  for  myopia  of  more  than  1  D. 

3.  The  speed  of  the  shadow  is  affected  by  the  movement  of 
the  mirror  itself  but  making  due  allowance,  the  speed  indicates 
if  the  error  is  high  or  low.  When  the  refractive  error  is  high,  there 
is  a  slow^ness  in  the  rate  of  movement  of  the  shadow  calling  for  a 
strong  lens  for  its  neutralization;  whereas,  when  the  movement 
seems  to  be  fast,  the  error  is  likely  to  be  low  and  call  for  a  weak 
lens. 


Where  is  the  observing  eye  iinth  the  concave  mirror  located  when 
the  shadow  movement  is  with  the  mirror? 

Beyond  the  point  of  reversal. 


How  is  the  shadow  movement  in  skiametry  affected  by  low 
degrees  of  ametropia?   Give  the  reason. 

In  low  forms  of  ametropia  the  movement  is  fast  because  of  the 
nearness  of  the  point  of  reversal.  The  nearer  to  the  point  of  re- 
versal the  faster  the  movement,  becaus,e  at  this  point  the  emergent 
rays  from  the  observed  eye  are  conjugate  to  the  observing  eye. 


Give  and  explain  the  reason  for  a  straight-lined  contour  of  the 
shadow  in  skiametry. 

A  straight  edge  of  the  shadow  indicates  astigmatism,  and  is 
due  to  the  fact  that  the  emergent  rays  from  the  observed  eye  are 
refracted  by  the  two  chief  meridians  of  the  eye,  one  of  least  and 
one  of  greatest  curvature,  and  as  a  result  the  focus  could  never 
be  round  or  a  point,  but  always  oval  or  a  line. 


What  kind  of  lens  should  be  placed  before  the  observed  eye  to 
produce  neutralization  when  the  observer  with  the  concave  mirror 
finds  a  shadow  movement  against  the  mirror? 

Convex. 


292  State  Board  Examinations 

With  respect  to  the  degree  of  ametropia  ivhat  may  be  deduced 
from  a  bright  retinal  reflex  in  skiametry? 

Ill  high  errors  the  reflex  is  ckill;    in  low  errors  it  is  bright. 


/;/  what  respect  does  the  dynamic  method  of  skiametry  differ 
from  the  static  method? 

In  static  skiametry  the  test  is  made  with  the  ciliary  muscle 
at  rest.  For  this  purpose  a  cycloplegic  is  sometimes  used  by 
medical  men,  while  optometrists  endeavor  to  get  the  same  result 
by  darkening  the  room  and  asking  the  patient  to  look  carelessly 
at  some  distant  object. 

Dynamic  skiametry  is  the  opposite  of  static,  and  signifies  the 
use  of  some  force,  which  in  the  case  of  the  eye  is  known  as  the 
accommodation.  The  test  is  made  while  the  accommodation  is 
in  action,  W'hich  is  done  by  asking  the  patient  to  read  test  letters 
placed  on  the  examiner's  brow  or  attached  to  his  mirror. 


In  static  skiametry  with  the  plane  mirror,  the  operator  working 
at  one  meter,  no  movement  of  the  shadow  is  found  in  the  vertical 
meridian;  ivith  a  1  D.  spheric  lens  placed  before  the  eye  there  is 
no  movement  of  the  shadow  in  the  horizontal  meridian.  State  the 
nature  and  the  amount  of  the  ametropia.  What  was  the  direction 
of  the  shadow  movement  when  the  mirror  was  rotated  horisotitally 
before  the  imposition  of  the  lens? 

If  with  plane  mirror  at  one  meter  no  movement  is  found  in 
vertical  meridian,  the  refraction  of  this  meridian  is  myopic  1  D. 
If  with  +  1  D.  lens  there  is  no  movement  in  the  horizontal 
meridian,  this  meridian  is  emmetropic.  The  case  then  is  one  of 
simple  myopic  astigmatism,  and  w^ould  be  corrected  by  a  —  1  D. 
cyl.  axis  180°. 

The  direction  of  the  shadow  in  the  horizontal  meridian  be- 
fore the  use  of  the  convex  lens,  would  be  "with." 


In    skiascopy    u'hat    two    points    are    conjugate  foci? 
The    retina    and    the    point    of    reversal. 


Retinoscopy  293 

With  the  plane  mirror,  what  is  the  direction  of  the  shadow 
movement  when  the  observer  is  within  the  point  of  reversal? 

With. 


In  dynamic  skiametry,  with  fixation  at  40  inches,  the  point 
of  reversal  in  the  vertical  meridian  is  found  at  16  inches,  +  2.50  D. 
lens  being  before  the  observed  eye  and  at  20  inches  in  the  horizontal 
meridian  until  —  1.25  D.  lens  before  the  observed  eye.  What  is  the 
kind  and  amount  of  ametropia? 

Mixed  astigmatism.  Vertical  meridian  hypermetropic  2  D. 
and  horizontal  meridian  myopic  2.25  D. 

Correcting  lens:  +  2  D.  cyl.  axis  180°  O  —  2.25  D.  cyl. 
axis  90°. 


Put  the  following  back  to  the  retinoscope  fijidings  after  reversing 
the  shadow  from,  40  inches:  —  .50  O    —  -25  X  50. 

If  we  reduce  this  sphero-cylinder  to  a  cross  cylinder,  we  have 
-  .50  D.  cyl.  axis  1.50  C   -  .75  D.  cyl.  axis  60° 
which  would  indicate  a  myopia  of  .50  D.  in  the  60th  meridian  and 
of  .75  D.  in  the  150th  meridian. 

Inasmuch  as  when  working  at  40  inches  we  must  add  —  ID. 
to  the  retinoscopic  findings,  therefore  the  latter  must  have  been 
+  .50  D.  in  the    60th  meridian 
+  .2S  D.  in  the  150th  meridian. 


Dark  room  findings: 

0.  D.  +  1.50  axis  90°  Z:  +3  axis  180° 
0.  S.    +  2.25  axis  90°  C  +  1-75  axis  180° 

Write  the  prescription. 

If  we  take  this  literally  and  make  allowance  for  a  working 
distance  of  1  D.,  the  prescription  would  be 

O.  D.  +  .50  D.  sph.  C  +  1.50  D.  cyl.  axis  180° 
O.  S.    +  .75  D.  sph.  C  +     .50  D.  cyl.  axis    90° 
But  usually  in  retinoscopy  we  find  the  lens  that  corrects 
each  meridian  and  then  we  have  to  deal  with  meridians  instead 
of  as  above  with  axes. 


294  State  Board  Examinations 

Usually  the  dark  room  findings  come  to  us  in  this  shape: 
O.  D.  +  1.50  vertically  —   +  3  horizontally, 
O.  S.    +2.25  vertically  —  +  1.75  horizontally, 
which  means  that  the  lenses  mentioned  neutralize  the  movement 
in  the  meridians  mentioned.    Then  making  the  allowance  of  1  D. 
and  remembering  that  axes  are  at  right  angles  to  meridians,  the 
prescription  would  read: 

O.  D.  +  .50  D.  sph.  C  +  1.50  D.  cyl.  axis    90° 
O.  S.    +  .75  D.  sph.  C   +     .50  D.  cyl.  axis  180° 


What  is  meant  by  the  statement  in  skiascopy  that  the  shadow 
moves  with  the  mirror,  or  the  shadoiv  moves  against  the  mirror? 

When  the  patient's  pupil  is  properly  illuminated  the  observer 
w'ill  see  a  bright  reflex  from  the  pupillary  area.  As  the  mirror 
is  turned  the  illumination  moves  off  followed  by  the  shadow, 
thus  causing  the  movement  of  the  shadow. 

The  illumination  on  the  patient's  face  always  moves  in  the 
same  direction  as  the  mirror  is  rotated,  but  not  necessarily  so  in 
the  pupil,  where  it  sometimes  appears  to  move  opposite,  and 
hence  w'e  speak  of  the  shadow  moving  "with"  or  "against"  the 
movement  of  the  mirror. 

What  characteristic  conditions  exist  when  the  point  of  reversal 
is  reached? 

At  the  point  of  reversal  no  definite  movement  of  the  retinal 
illumination  can  be  made  out,  and  while  the  pupil  is  uniformly 
illuminated  it  shows  a  duller  reflex  than  when  within  or  beyond 
this  point,  and  the  shadow  will  be  absent. 


What  difference  is  observed  in  the  directions  of  the  movement 
of  the  facial  and  retijial  illuminations  by  the  plane  and  the  concave 
mirror   respectively? 

The  movement  on  the  face  is  always  the  same  as  the  mirror, 
whether  it  be  convex  or  concave. 

In  the  pupil  the  movements  caused  by  the  plane  and  the 
concave  mirror  are  the  reverse  of  each  other,  and  they  also  vary 
with  the  condition  of  refraction. 


Retinoscopy  295 

In  emmetropia,  hypermetropia  and  myopia  less  than  1  D. 
the  movement  is  with  when  using  a  plane  mirror  and  against 
when  using  a  concave  mirror. 

In  myopia  greater  than  1  D.  the  movement  is  against  with 
a  plane  mirror  and  with  when  using  a  concave. 


With  respect  to  the  point  of  reversal,  ivhere  must  the  observer 
be  located  to  see  (a)  the  shadow'  movement  directed  the  same  as  the 
plane  mirror;  (b)  the  shadoiv  movement  directed  opposite  to  the 
plane  mirror;  (c)  the  shadow  movement  directed  the  same  as  the 
concave  mirror;  id)  the  shadoiv  movement  directed  opposite  to  the 
concave  mirror? 

a.  Inside  the  point  of  reversal. 

b.  Outside  the  point  of  reversal. 

c.  Outside  the  point  of  reversal. 

d.  Inside  the  point  of  reversal. 


What  may  be  discovered  by  dynamic  skiametry?  In  what 
respect  does  the  dynamic  method  differ  from  the  static  method? 

The  object  of  dynamic  method  is  to  discover  spasm  of  the 
accommodation.  It  differs  from  the  static  method  in  that  a 
definite  amount  of  accommodation  is  brought  into  action  accord- 
ing to  the  distance  of  the  point  of  fixation,  whereas  in  the  static 
method  the  effort  is  to  keep  the  accommodation  at  rest. 


Which  focal  point  is  sought  to  be  determined  by  skiametry  and 
what  relation  exists  between  it  and  the  retina  of  the  observed  eye? 

The  anterior  focal  point  which  would  be  conjugate  to  the 
retina  of  the  eye  under  observation. 


Describe  the  respective  shadow'  movement  with  the  plane  and 
concave  mirror,  and  state  the  advantage,  if  any,  of  the  former  over 
the  latter? 

With  the  plane  mirror  the  shadow  movements  are  in  the 
same  direction   as   the   movements  on   the   face  when   the  eye 


296  State  Board  Examinations 

(if  observer  is  inside  the  point  of  reversal,  and  in  the  opposite 
direction  to  the  movements  on  the  face  when  the  observer's  eye 
is  beyond  the  point  of  reversal. 

The  mo\ements  caused  by  a  concave  mirror  are  just  the 
reverse  in  each  case  to  those  caused  by  a  plane  mirror. 

The  advantages  of  the  plane  mirror  are  that  it  is  simpler 
and  easier  and  can  be  used  at  any  distance,  whereas  with  the 
concave  mirror  the  eye  under  observation  must  be  at  such  a 
distance  that  the  rays  of  light  from  the  mirror  come  to  a  focus 
and  cross  before  entering  it. 


How  does  the  observer  decide  that  the  point  of  reversal  has  been 
reached? 

The  point  of  reversal  is  reached  when  the  movements  have 
been  neutralized,  or  when  it  is  impossible  to  determine  in  which 
direction  the  shadow  appears  to  move.  This  is  not  always  an 
easy  matter,  and  the  ability  to  quickly  find  the  point  of  reversal 
comes  only  after  extended  practice. 

Perhaps  the  better  way  for  a  beginner  is  to  make  or  estimate 
between  the  lens  that  just  makes  the  movement  with  and  one 
that  just  turns  it  against.  For  instance,  if  with  +  2  D.  the  move- 
ment is  still  with  and  with  +  2.50  the  movement  has  turned 
against,  we  have  narrowed  the  point  of  reversal  down  to  a  point 
between  the  strength  of  these  two  lenses. 


Describe  the  appearance  of  the  retinal  illumination  in  pro- 
nounced astigmatism. 

As  a  band  of  light  which  is  characteristic  of  astigmatism. 
If  the  spherical  error  be  high  and  the  astigmatism  slight,  the  band 
of  light  will  not  be  noticeable  on  first  inspection,  not  until  the 
axial  error  has  been  at  least  partly  corrected,  and  becomes 
brightest  when  fuUv  corrected. 


Describe  the  directions  of  the  real  movement  of  the  facial  and 
retinal  illuminatioris  by  the  plane  and  the  concave  mirror  respec- 
tively. 


Retinoscopy  297 

The  facial  illumination  is  always  in  the  same  direction  as 
the  movement  of  the  mirror,  whether  it  be  plane  or  concave. 

With  a  plane  mirror  the  retinal  illumination  is  always  in 
the  same  direction  as  the  movement  of  the  mirror,  whether  the 
case  be  one  of  emmetropia,  hypermetropia  or  myopia.  The 
concave  mirror  causes  re\erse  movements. 


Describe  the  directions  of  the  apparent  movement  of  the  facial 
and  retinal  illuminations  by  the  plane  and  the  concave  mirror 
respectively. 

The  apparent  movement  of  the  retinal  illumination  depends 
upon  whether  the  observer  i'^;  ^vithin  or  beyond  the  point  of 
reversal,  or  the  point  conjugate  to  the  retina  of  the  observed  eye. 

Using  a  plane  mirror  if  the  observer  is  within  the  point  of 
reversal  (as  in  emmetropia  and  hypermetropia)  the  movements 
will  be  with.  If  obser\-er  is  beyond  the  point  of  reversal  (as  in 
myopia  greater  than  1  D.)  the  movements  will  be  against. 

Using  a  concave  mirror,  if  the  observer  is  within  the  con- 
jugate point,  the  movements  will  be  against;  if  beyond  the 
conjugate  point,  with. 

Explain  the  dynamic  method  of  skiametry.  State  the  purpose 
of  this  method. 

In  the  dynamic  method  of  skiametry  a  card  of  letters  is 
attached  to  the  retinoscope  or  placed  on  the  brow  of  the  examiner, 
at  which  the  patient  is  asked  to  look,  after  which  lenses  are  used 
in  the  customary  way  to  find  the  point  of  reversal. 

In  this  method  a  definite  amount  of  accommodation  is  used, 
depending  upon  the  distance  of  fixation,  in  this  way  reducing  the 
tendency  to  spasm.  The  test  can  be  made  at  any  distance,  and 
the  result  represents  the  amount  of  defect,  no  allowance  to  be 
made  for  the  working  distance. 


//  with  the  plane  mirror  before  the  static  eye.  a  shadow  move- 
ment against  the  mirror  is  neutralized  in  the  horizontal  meridian 
by  —  ID.  lens  of  40  inches  and  in  the  vertical  meridian  by  the 
same  lens  at  30  inches  (a)  what  wnll  be  the  movement  at  20  inches? 
(b)  'what  is  the  amount  of  ametropia? 


298  State  Board  Examinations 

As  the  mirror  must  be  moxed  up  to  30  inches  in  order  to 
neutraHze  the  vertical  meridian,  this  meridian  must  be  .2>2>  D. 
more  myopic.  As  the  rule  is  to  add  —  1  D.  to  the  retinoscopic 
findings,  we  have  —  2  D.  as  the  measure  of  the  horizontal 
meridian,  and  —  2.33  D.  as  the  measure  of  the  vertical  meridian. 
This  is  a  case  of  compound  myopic  astigmatism,  and  the  correct- 
ing lens  would  be 

-2D.  sph.  C   -  .2>2,  D.  cyl.  axis  180° 

At  20  inches  there  would  be  no  movement  in  the  horizontal 
meridian  because  neutralized  by  the  2  D.  of  myopia  in  this 
meridian,  while  in  the  \'ertical  meridian  there  would  be  a  move- 
ment aminst. 


With  a  -^  1  D.  lens  before  the  static  eye  and  the  plane  mirror 
at  1  meter  the  shadotv  movement  is  ivith  the  mirror  in  the  horizontal 
and  against  it  in  the  vertical  meridian;  it  is  also  found  that  there 
are  other  superposed  lenses  of  1  D.,  each  of  ivhich  separately  neutral- 
izes these  movements.  Give  the  character  of  the  ametropia  and  of 
the  lens  that  corrects  it. 

If  with  +  1  D.  lens  before  the  static  eye,  to  neutralize  the 
distance,  the  mo\ement  is  with  in  the  horizontal  meridian,  hyper- 
metropia  is  proven,  and  if  this  movement  is  neutralized  by 
another  1  D.  lens,  it  must  be  a  +  1  D.,  which  would  be  the 
measure  of  this  meridian. 

If  in  the  vertical  meridian  the  movement  is  against  myopia 
is  proven,  and  if  this  movement  is  neutralized  by  a  1  D.  lens 
it  must  be  a  —  1  D.  lens,  which  would  be  the  measure  of  this 
meridian. 

The  case  is  therefore  one  of  mixed  astigmatism  and  the 
correcting  cross-cylinder  would  be 

+  1  D.  cyl.  axis  90°  C   -  1  D.  cyl.  axis  180° 
which  can  be  transposed  to 

-  1  D.  sph.  C   +  2  D.  cyl.  axis  90° 


A  patient,  while  wearing  —  2D.  sph.  lenses  under  the  dynamic 
test,  neutralizes  the  shadow  movement  during  fixation  up  to  40  cm. 
Give  his  amplitude  of  accommodation  and  the  distance  of  his  near 
point  without  glasses. 


Retinoscopy  299 

In  order  to  neutralize  the  moxement  at  40  cm.  2.50  D.  of 
accommodation  is  necessary,  and  as  a  further  2  D.  of  accom- 
m.odation  must  be  used  to  overcome  the  —  2D.  lenses  worn, 
the  amplitude  of  accommodation  must  be  4.50  D.,  which  would 
represent  a  near  point  of  9  inches. 


A  young  hyperope,  having  normal  acnteness  of  vision,  either 
uith  or  without  +  0.5  D.  le?ises,  being  subjected  to  the  dynamic 
test,  is  found  to  require  -\-  1  D.  lenses  to  arrest  motion  of  the  shadow 
for  all  proximate  distances  up  to  25  cm.  Which  lenses  should  be 
given  him  for  reading? 

The  +  .50  D.  lenses  represent  the  amount  of  manifest 
hypermetropia  as  measured  by  the  trial  case,  and  +  1  D.  the 
amount  of  total  error  as  measured  by  the  dynamic  method  of 
retinoscopy. 

Theoretically  it  would  be  proper  to  give  him  the  full  correc- 
tion of  +  1  D.  for  reading,  but  practically  it  is  sometimes  advis- 
able in  young  people  to  slightly  undercorrect. 


By  static  retinoscopy  at  40  inches  the  vertical  meridian  of  the 
eye  is  found  to  neutralize  with  a  -{-  1.75,  and  the  horizontal  meridian 
with  a  +  1.50.     What  is  the  correction  for  distance? 

After  making  allowance  for  the  working  distance  of  40 
inches  the  refraction  of  the  vertical  meridian  is  hypermetropic 
.75  D.  and  of  the  horizontal  meridian  .50  D.  The  correcting 
lens  would  be 

+  .50  D.  sph.  C  +  .25  D.  cyl.  axis  180° 


If  a  person  has  an  error  of  —  1  on  -\-  2  cyl.  axis  45° ,  what 
movements  of  shadows  will  be  observed  ivith  the  plane  retinoscope? 

Assuming  the  test  is  made  at  a  distance  of  40  inches,  then 
in  the  meridian  of  the  axis  of  the  cylinder  there  would  be  no 
motion  on  account  of  the  1  D.  of  myopia,  while  in  the  135th 
meridian  the  motion  would  be  with  the  mirror. 


v^OO  State  Board  Examinations 

hi  Hsinii  the  reti)!Oscope  with  plane  mirror,  what  causes  the 
shadow,  and  why  in  hyperopia  does  the  shadoiv  move  ivith  the 
mirror? 

In  retinoscopy  light  is  reflected  by  means  of  a  mirror  into 
the  patient's  eye  where  it  falls  upon  the  retina,  making  an  area 
of  light,  which  constitutes  the  retinal  illumination.  The  shadow 
is  the  non-illuminated  portion  of  the  retina  immediately  sur- 
rounding the  illumination. 

In  hypermetropia  the  rays  emerge  divergenth-,  consequently 
the  focus  of  such  an  eye  is  beyond  the  observer,  in  fact  it  is  even 
beyond  infinity;  therefore,  according  to  the  laws  of  optics  under 
such  conditions,  the  shadow  must  move  with  the  mirror. 


In  static  skiametry,  if  the  patient  has  1  D.  of  myopic  astig- 
matism in  vertical  meridian,  at  what  distance  will  the  neutral  point 
be  located  in  the  horizontal  meridian  with  a  -[-  1  D.  lens  placed 
before  the  eye? 

The  patient  has  1  D.  of  myopic  astigmatism  in  the  vertical 
meridian  while  the  horizontal  meridian  is  emmetropic.  A  +  1  D- 
lens  placed  before  the  eye  would  locate  the  neutral  point  of  the 
latter  at  one  meter,  which  is  just  the  position  of  the  retina  of  the 
observer.  This  is  just  the  same  as  in  emmetropia  where  +  1  D. 
lens  is  necessarv  to  neutralize  the  movements  at  one  meter. 


With  a  -\-  3  D.  lens  before  the  static  eye,  where  ivill  the  neutral 
point  in  the  horizontal  and  vertical  meridians  be  located  for  the 
ametrope  ivhose  correction  is  -\-  1  D.  sph.  Z^   -\-  1  D.  cyl.  axis  90°? 

In  this  case  the  correcting  combination  would  show  that 
there  was  +  1  D.  of  hypermetropia  in  the  vertical  meridian, 
and  2  D.  of  hypermetropia  in  the  horizontal  meridian.  Placing 
a  -|-  3  D.  lens  before  such  an  eye  would  make  the  vertical  me- 
ridian myopic  to  the  extent  of  2  D.  which  would  cause  the  neutral 
point  to  be  located  at  20  inches.  The  -(-3D.  lens  would  make 
the  horizontal  meridian  myopic  to  the  extent  of  1  D.  thus  causing 
its  neutral  point  to  be  located  at  40  inches. 


Retinoscopy  301 

What  is  the  fundamental  principle  of  the  test  icith  the  skiascope? 

The  principle  of  retinoscopy  is  to  find  the  point  of  reversal 
or  the  far  point  which  either  occurs  naturally  as  in  myopia  or 
is  artificially  produced  by  convex  lenses. 


Which  focal  point  is  sought  in  the  examination  ivith  the  retino- 
scope,  and  what  is  the  relation  of  that  point  with  the  retina  of  the  eye? 

The  point  of  re\'ersal  A\here  no  motion  is  evident.  This  is 
the  far  point  of  the  eye,  naturally  so  in  myopia  and  artificially 
produced  by  convex  lenses  in  hypermetropia,  and  is  conjugate  to 
the  retina. 


In  static  skiametry  ivith  the  plane  mirror  the  operator,  working 
at  one  meter,  no  movemeyit  of  the  shadow  is  found  in  the  vertical 
meridian;  with  a  -\-  1  D.  sphere  placed  before  the  eye  there  is  no 
movement  of  the  shadow  in  ilie  horizontal  meridian.  State  the 
nature  and  the  amount  of  the  ametropia.  What  was  the  direction 
of  the  shadow  movement  when  the  mirror  was  rotated  horizontally 
before  the  imposition  of  the  lens? 

Under  the  conditions  named  no  movement  of  the  shadow 
would  show  a  myopia  of  1  D.  in  the  vertical,  and  a  neutralization 
of  the  movement  by  a  +  1  D.  emmetropia  of  the  horizontal 
meridian.  This  would  indicate  a  myopia  of  1  D.  with  the  rule 
and  would  be  corrected  by  —  ID.  cyl.  axis  180°. 

The  direction  of  the  shadow  movement  in  the  horizontal 
meridian  before  the  imposition  of  the  +  1  D.  lens  must  have 
been  with  the  light. 

In  static  skiametry  if  the  patient  has  1  D.  of  myopic  astigma- 
tism, correcting  lens  axis  vertical,  at  what  distance  will  the  point 
of  reversal  be  located  in  the  horizontal  meridian  with  -\-  I  D.  placed 
before  the  eye? 

If  the  axis  of  the  correcting  cylinder  is  vertical  the  defective 
meridian  is  horizontal,  being  myopic  to  the  extent  of  1  D.  A  + 
1  D.  placed  before  the  eye  will  make  this  horizontal  meridian 
myopic  that  much  more,  and  the  point  of  reversal  will  then  be 
located  at  20  inches. 


302  State  Board  Examinations 

Since  the  layers  that  make  up  the  retina  of  the  eye  are  trans- 
parent Jiow  is  it  possible  that  we  can  see  a  reflex  in  retinoscopy? 

Inasmuch  as  the  retina  has  a  pigment  layer  and  besides  is 
in  close  contact  with  the  dark-colored  choroid  the  light  that  is 
thrown  into  the  eye  is  reflected  from  the  retina  and  shows  in 
the  pupil  as  a  bright-colored  reflex. 


Why  do  we  seek  in  skiascopy  to  get  neutrality  of  motion  of  the 
light  reflex? 

In  order  to  find  the  point  of  reversal,  which  is  the  principle 
of  retinoscopy,  and  by  which  the  refraction  of  the  eye  is  deter- 
mined. 

Why  is  it  in  skiascopy  that  it  is  not  always  possible  to  find 
neutrality  of  motion  of  the  light  reflex? 

On  account  of  irregularity  of  curvature  of  the  crystalline 
lens  or  cornea. 

What  is  meant  in  skiascopy  by  the  term  ''with  the  mirror?'' 

That  the  movement  of  the  retinal  reflex  in  the  pupil  is  in 
the  same  direction  as  the  movement  of  the  light  on  the  face. 


What  is  the  appearance  of  the  light  in  the  pupil  when  there  is 
astigmatism? 

As  a  band  of  light. 

Working  with  the  plane  mirror  the  vertical  meridian  is  neutral 
at  one  meter  and  the  horizontal  meridian  at  half  meter.  What  will 
be  the  movements  in  the  two  meridians  at  half  meter? 

The  vertical  meridian  is  shown  to  be  myopic  1  D.  and  the 
horizontal  meridian  myopic  2  D.  At  half  meter  the  movements 
in  the  vertical  meridian  would  be  with,  while  the  horizontal 
meridian  will  be  neutral. 

In  a  certain  eye  the  motion  of  one  principal  meridian  is  slightly 
against,  while  that  of  the  other  is  slightly  with.     What  will  be  the 


Retinoscopy  303 

effect  of  putting  in  front  of  the  eye  a  high-power  plus  lens?    Also  the 
effect  of  using  a  high-power  minus  lens? 

This  would  be  a  mild  case  of  mixed  astigmatism.  A  strong 
convex  lens  would  make  both  meridians  myopic,  and  the  motion 
would  be  against  in  both.  A  strong  concave  lens  would  make 
both  meridians  hypermetropic,  and  the  motion  would  be  with 
in  both,  presuming  a  plane  mirror  is  used. 


A  patient  who  is  1  D.  hypermetropic  and  tvhose  near  point  is 
at  13  inches  requires  a  -\-  2  D.  lens  to  shoiu  neutral  motion  by  the 
dynamic  method  at  20  inches.     What  conclusions  woidd  you  draw? 

That  there  was  a  hypermetropia  of  at  least  2  D. 


What  is  the  difference  between  a  static  test  and  a  dynamic  test? 

In  a  static  test  the  ciliary  muscle  is  supposed  to  be  passive 
or  at  rest,  as  in  the  objective  tests.  In  a  dynamic  test  the  ciliary 
muscle  is  an  action,  as  in  the  subjective  tests. 


A  child  shows  by  the  static  test  with  the  skiascope  an  error 
of  +  50  D.  and  by  the  dynamic  test  made  at  16  inches  he  shows  an 
error  of  +  1.25  D.     What  glasses  woidd  you  recommend,  and  why? 

The  dynamic  test  shows  that  with  a  relaxation  of  accom- 
modation the  error  is  equal  at  least  to  1.25  D.  We  hardly  think 
it  advisable,  however,  to  prescribe  so  full  a  correction  on  account 
of  the  strong  accommodation  of  youth.  We  would  be  inclined 
to  make  a  compromise  and  order  about  +  .75  D.,  if  it  seemed 
necessary  to  order  glasses  at  all. 


A  patient  sixty  years  of  age  shows  by  the  static  method  with 
the  skiascope  2  D.  of  hypermetropia  and  by  the  dynamic  method 
at  20  inches  a  -\-  4  D.  is  required  to  neutralize  motion.  What  is 
the  prescription  for  distance  and  for  reading  at  16  inches? 

+  2  D.  for  distance,  -f  4.50  D.  for  reading. 


304  State  Board  Examinations 

Why  are  the  movements  of  the  edge  of  the  light  reflex  in  skia- 
scopy in  reversed  directions,  according  as  the  plane  or  concave 
mirror  is  used^ 

Because  in  the  case  of  the  concave  mirror  the  ra>s  of  light 
ha\-e  been  brought  to  a  focus  and  diverged. 


What  is  the  difference  in  the  real  movement  of  the  retinal 
illumination  in  skiascopy  and  the  apparent  movement? 

The  real  mo\'ement  corresponds  to  the  mo\"ement  of  the 
retinoscope,  while  the  apparent  movement  is  dependent  on  the 
location  of  the  focus,  whether  in  front  of  or  behind  the  instru- 
ment. 

At  what  point  is  the  astigmatic  hand  the  most  noticeable? 

The  band  of  light  is  seen  when  one  meridian  is  corrected 
and  the  meridian  at  right  angles  remains  uncorrected  or  only 
partly  corrected. 

When  the  astigmatism  is  relatively  high  and  the  spherical 
error  of  small  amount  the  band  of  light  is  usually  evident  on  first 
inspection  before  any  neutralizing  lens  is  placed  in  position. 


When  does  the  edge  of  light  reflex  move  the  most  rapidly,  in 
high  or  in  low  errors? 

When  the  refractive  error  is  slight  and  a  weak  lens  is  required 
for  its  correction  the  movement  is  fast. 


Upon  what  principle  or  principles  is  retinoscopy  based?  What 
is  the  scissors  movement? 

The  principle  of  retinoscopy  is  the  finding  of  the  point  of 
reversal,  or  the  far  point  of  a  myopic  eye,  either  naturally  myopic 
or  made  so  artifically  by  means  of  convex  lenses  that  will  bring 
the  emergent  rays  of  light  to  a  focus  at  some  definite  distance. 

In  the  so-called  scissors  movement  there  are  two  areas  of 
light,  or  two  shadows  seen  in  the  same  meridian,  occurring  usually 
in  astigmatism,  and  especially  in  irregular  astigmatism.     The 


Retinoscopy  305 

cause  of  the  scissors  movement  is  mostly  attributed  to  a  slight 
tilting  of  the  crystalline  lens. 


In  using  the  retinoscope  ivhat  glasses  would  you  wear  in  order 
to  get  the  best  results,  and  why  is  it  necessary  to  wear  glasses  at  alii' 

The  reason  why  it  is  necessary  for  the  observer  to  wear 
glasses,  and  the  only  reason,  is  that  he  may  get  the  clearest  view 
of  the  patient's  pupil.  For  this  purpose,  if  the  observer  have 
sufficient  amplitude  of  accommodation,  his  distance  glasses  will 
answer  until  an  age  is  reached  when  there  is  but  little  accom- 
modation left,  and  then  a  convex  lens  must  be  added  that  will 
afford  sharp  vision  at  40  inches. 


In   skiametry  why  is  the  point  of  reversal  conjugate  to  the 
retina  of  the  observed  eye? 

Because  it  is  the  neutral  point,  and  the  rays  diverging  from 
which  would  exactly  focus  on  the  retina  of  the  eye. 


Why  is  the  plane  mirror  generally  given  preference  over  the 
concave  mirror? 

With  the  plane  mirror  the  test  can  be  made  at  any  distance, 
whereas  with  the  concave  mirror  care  must  be  taken  to  see  that 
the  distance  be  greater  than  the  focus  of  the  mirror. 


What  is  the  difference  of  movement  of  the  light  edge  -with  plane 
mirror  as  compared  with  the  concave  mirror? 

Just  the  reverse.  In  emmetropia  and  hypermetropia  where 
the  plane  mirror  shows  a  with  movement  the  concave  mirror 
will  show  an  against  movement.  In  myopia  where  the  plane 
mirror  shows  an  against  movement  the  conca\'e  mirror  will  show 
a  with  movement. 

When  is  the  retinal  reflex  the  brightest  with  the  plane  mirror, 
and  when  with  the  concave  mirror? 

With  both  mirrors  close  to  the  point  of  re\-ersal. 


306  Slate  Board  Examinations 

When  does  the  light  spot  on  the  retina  move  the  fastest,  when 
the  reflex  is  near  or  far  from  the  neutral  point? 

Near  the  neutral  point. 


What  are  the  characteristics  of  the  light  reflex  at  the  reversal 
point  in  the  human  eye? 

No  definite  movement  of  the  retinal  illumination  can  be 
made  out,  and  the  pupillary  area  is  seen  to  be  uniformly  illumi- 
nated. 

On  what  does  the  real  movement  of  the  retinal  reflex  depend? 

On  the  direction  in  which  the  light  is  made  to  go  by  the 
tilting  of  the  mirror. 

On  what  does  the  apparent  movement  of  the  retiyial  reflex 
depend? 

On  the  character  of  the  emergent  rays. 


When  the  observer  is  nearer  than  the  neutral  point,  what  will 
he  the  direction  of  the  shadow  movement  with  the  plane  mirror? 

With. 


When  the  observer  is  farther  away  then  the  neutral  point,  what 
will  be  the  direction  of  the  movement  with  the  concave  mirror? 

With.  . 

In  retinoscopy  by  the  usual  static  method,  if  the  patient  has 
2  D.  of  hypermetropic  astigmatism,  axis  vertical,  at  what  distance 
will  the  point  of  reversal  be  located  in  the  horizontal  meridian  with 
a  -{-  3  D.  sphere  placed  before  the  eye? 

If  the  axis  of  the  correcting  cylinder  is  vertical,  the  2  D. 
of  hypermetropic  astigmatism  would  exist  in  the  horizontal 
meridian.  A  +  3  D.  sphere  placed  before  the  eye  would  over- 
correct  this  meridian  and  make  it  myopic  to  the  extent  of  1  D., 
in  which  case  the  point  of  reversal  would  be  located  at  one 
meter  or  40  inches. 


Retinoscopy  307 

In  retinoscopy  by  the  usual  static  metJiod,  with  a  -\-  2D.  lens 
before  the  eye,  uhere  icill  the  point  of  reversal  in  the  vertical  and 
horizontal  meridia^is  be  located  for  the  ametrope  ivhose  correction  is 
-2D.  sph.  -ID.  cyl.  axis  180°? 

This  is  a  case  of  compound  myopic  astigmatism  in  which 
naturally  the  point  of  reversal  for  the  vertical  meridian  would 
be  located  at  13  inches  and  for  the  horizontal  meridian  at  20 
inches.  The  addition  of  a  +  2  D.  before  the  eye  would  increase 
the  myopia  to  that  extent,  and  then  the  point  of  reversal  for  the 
vertical  meridian  would  be  moved  up  8  inches  and  for  the  hori- 
zontal meridian  to  10  inches. 


Using  the  method  of  dynamic  skiametry  and  working  at  40 
inches,  a  -\-  1  D.  sphere  causes  reversal  in  the  vertical  meridian, 
while  it  requires  a  +  1-50  D.  to  cause  reversal  in  the  horizontal 
meridian,  what  is  the  kind  and  amount  of  ametropia? 

In  accordance  with  the  theory  of  dynamic  skiametry  in 
which  no  allowance  is  to  be  made  for  the  distance  at  which  the 
test  is  made,  this  case  would  be  one  of  compound  hypermetropic 
astigmatism,  showing  1  D.  of  defect  in  the  vertical  meridian 
and  1.50  D.  of  defect  in  the  horizontal  meridian,  and  the  correct- 
ing lens  would  be  +  1  D.  sph.  —  +  -50  D.  cyl.  axis  90°. 


An  eye  tested  with  the  retinoscope  by  the  customary  static 
method  shows  the  following:  Vertical  meridian  point  of  reversal 
at  18  inches  and  horizontal  meridian  point  of  reversal  of  32  inches. 
What  is  the  refractive  condition  of  each  meridian,  ivhat  two  sphero- 
cylinders  may  be  prescribed  for  distance,  and  which  one  ivould  you 
consider  best? 

Vertical  meridian  myopic  2.25  D.,  and  horizontal  meridian 
myopic  1.25  D. 

The  correcting  sphero-cylinders  are: 

-  1.25  D.  sph.  =   -  1  D.  cyl.  axis  190° 

-  2.25  D.  sph.  -   +  1  D.  cyl.  axis    90° 

The  latter  would  be  considered  best,  because  more  periscopic 
and  with  a  vertical  axis. 


308  State  Board  Examinations 

With  a  +  1.50  in  the  trial  frajne,  the  45th  meridian  of  an  eye 
shows  the  point  of  reversal  at  27  inches,  at  the  same  time  the  motion 
in  the  135th  meridian  is  uith.  By  changing  the  +  1-50  to  +  2.75 
the  point  of  reversal  in  this  latter  meridia?!  is  found  to  be  at  40  inches. 
What  is  the  refractive  condition  of  each  meridian,  and  what  two 
sphero-cylinders  may  be  prescribed? 

When  the  test  is  made  at  27  inches,  we  must  add  —  1.50  D. 
to  the  lens  that  produces  reversal,  which  in  this  case  is  equivalent 
to  piano,  showing  the  45th  meridian  to  be  emmetropic. 

When  the  test  is  made  at  40  inches,  we  must  add  —  1  D.  to 
the  lens  that  produces  reversal,  which  in  this  case  would  show  a 
hypermetropia  of  1.75  D.  in  the  135th  meridian. 

The  correcting  lens  would  be  a  piano-cylinder: 
+  1.75  D.  cyl.  axis  45°, 
which,  however,  may  be  transposed  into  a  sphero-cylinder: 
+  1.75  D.  sph.  =   -  1.75  D.  cyl.  axis  135°. 


With  the  retinoscope  at  a  distance  of  40  inches  from  the  eye 
as  in  the  usual  static  method,  a  +  5.50  D.  lens  is  required  to  neutral- 
ize the  120th  meridian,  and  a  —  .50  D.  to  neutralize  the  30th 
meridian.     What  is  the  amount  of  astigmatism  present  in  the  eye? 

This  is  ascertained  by  finding  the  difference  between  the 
two  cylinders,  or  subtracting  one  from  the  other,  which  in  this 
case,  where  one  is  plus  and  the  other  minus,  would  show  6  D.  of 
astigmatism. 

Suppose  the  15th  meridian  of  an  eye  is  emmetropic  and  the 
105th  meridian  is  2.50  D.  hypermetropic;  where  is  the  point  of 
reversal  of  each  meridian  ivhen  a  —  .50  D.  lens  is  placed  before  the 
eye? 

In  the  emmetropic  meridian  the  point  of  reversal  is  at 
infinity,  and  in  the  hypermetropic  meridian  beyond  infinity. 
A  —  .50  lens  would  make  the  point  of  re\'ersal  in  the  emmetropic 
meridian  beyond  infinity,  and  in  the  hypermetropic  meridian 
still  further  beyond. 

With  a  +  2.50  D.  lens  in  the  trial  frame  the  point  of  reversal 
of  the  30th  meridian  of  an  eye  under  test  by  the  usual  static  method 


Retinoscopy  309 

of  the  retinoscope  is  found  to  be  32  inches.  Changing  the  lens  in 
the  frame  to  a  -\-  1.25  the  point  of  reversal  in  the  120th  meridian  is 
found  at  32  inches.  What  kind  of  astigmatism  is  present  and  what 
is  its  amount.'^ 

We  must  make  allowance  for  the  distance  at  which  the  test 
is  made,  adding  a  minus  lens  which  corresponds  to  this  distance. 
The  lens  which  represents  the  working  distance  of  32  inches  is 
1.25  D.;  therefore,  we  must  add  —  1.25  to  the  finding  in  each 
meridian.  Adding  —  1.25  to  +  2.50  would  show  the  30th 
meridian  to  be  hypermetropic  to  the  extent  of  1.25  D.  Adding 
—  1.25  to  +  1.25  would  show  neutralization  and  indicate  the 
120th  meridian  to  be  normal. 

Therefore  it  is  a  case  of  simple  hypermetropic  astigmatism, 
and  the  correcting  lens  is  +  1.25  D.  cyl.  axis  120°. 


With  a  -\-  6  lejts  before  the  patient's  eye  the  point  of  reversal 
for  the  150th  meridian  is  at  32  inches;  for  the  60th  meridian  at  16 
inches.     What  would  be  the  correction  for  distanced 

To  make  allowance  for  the  working  distance  of  il  inches, 
we  must  add  —  1.25  D.  to  the  neutralizing  lens  +  6  D.,  which 
shows  a  hypermetropia  of  4.75  D.  in  the  150th  meridian.  For 
the  distance  of  16  inches  we  add  —  2.50  D.  to  the  same  neutraliz- 
ing lens,  which  shows  a  hypermetropia  of  3.50  in  the  60th  me- 
ridian.    This  would  call  for 

+  4.75  D.  cyl.  axis  60°  C   +  3.50  D.  cyl.  axis  150°, 
or, 

+  3.50  D.  sph.  C   +  1.25  D.  cyl.  axis  60°. 


Working  at  a  distance  of  40  inches  the  retinoscopic  finding  for 
the  180th  meridian  of  an  eye  is  +  5  and  for  the  90th  meridian  it  is 
+  6.  What  would  be  the  equivalent  sphero-cylinders  for  distance 
correction? 

To  make  allowance  for  the  working  distance  of  40  inches 
we  must  add  —  1  D.  to  both  meridians,  which  would  show  the 
180th  meridian  to  be  hypermetropic  4  D.  and  the  90th  meridian 
hypermetropic  5  D.,  which  would  call  for 


310  State  Board  Examinations 

+  4  D.  cyl.  axis  90°  C  +  5  D.  cyl.  axis  180°, 
or, 

+  4  D.  sph.  C   +  1  D.  cyl.  axis  180°. 


Working  at  a  distance  of  27  inches  from  the  eye  in  the  static 
method  of  retinoscopy,  the  J 5th  meridian  needs  a  +  2.50  D.  to  get  a 
choked  disk,  while  the  105th  meridian  needs  +  3.50  D.  The  full 
correction!  for  distance  is  prescribed  and  torics  are  ordered.  On 
testing  the  torics  with  a  lens  measure  one  surface  is  found  to  be  a 
—  7 .50  D.  sphere;  on  the  other  surface  the  15th  meridian  shoics  + 
8.50  and  the  105th  meridian  shoivs  -\-  .50.  Has  the  prescription 
been  correctly  filled.^ 

In  working  at  27  inches  we  must  add  —  1.50  D.  to  the  lens 
that  produces  neutralization,  which  would  show  a  hypermetropia 
of  1  D.  in  the  15th  meridian  and  of  2  D.  in  the  105th  meridian. 
In  estimating  the  power  of  the  toric  lens  we  find  that  the  concave 
surface  against  the  convex  curves,  leaves  just  the  proper  amount 
of  convexity  in  each  meridian  to  correct  its  hypermetropia. 
Hence  the  prescription  has  been  correctly  filled. 


To  zvhat  retinoscopic  findings  at  one  meter  woidd  a  +  ^  O  — 
1.25  cylinder  axis  90°  correspond? 

This  prescription  when  analyzed  shows  a  hypermetropia  of 
2  D.  in  the  vertical  meridian  and  of  +  .75  D.  in  the  horizontal. 
Inasmuch  as  working  at  one  meter  a  —  1  D.  must  have  been 
added  to  obtain  this  prescription,  so  now  we  must  add  +  1  D. 
to  find  the  neutralizing  lenses,  which  would  show  the  retinoscopic 
findings  to  be  +  3  D.  vertically  and  +  1.75  D.  horizontally. 


With  a  -\-  6  D.  sphere  before  the  patient's  eye,  the  135th  me- 
ridian shoivs  the  point  of  reversal  at  40  inches,  and  the  45th  meridiait 
shows  the  same  at  a  distance  of  8  inches.  What  would  be  the  distance 
correction? 

As  the  point  of  reversal  in  the  135th  meridian  is  at  40  inches, 
we  add  —  1  D.  to  the  +  6  D.,  showing  a  hypermetropia  of  5  D. 
in  this  meridian.     The  point  of  reversal  in  the  45th  meridian 


Retinoscopy  311 

being  at  8  inches,  we  add   —   5  D.  to  the   +   6  D.,  showing  a 
hypermetropia  of  1  D.  in  this  meridian. 

The  correction  for  distance  would  be  +  1  D.  sph.  O  +  -i  D. 
cyl.  axis  45°. 

//  the  findings  for  distance  by  the  retinoscope  are  +  1.25  for 
the  60th  meridian  and  +  1.75  for  the  150th  meridian,  ivhat  two 
sphero-cylinders  may  be  prescribed? 

Assuming  the  examination  was  made  at  one  meter,  and 
adding  —ID.  for  this  distance,  we  find  a  hypermetropia  of 
.25  D.  in  the  60th  meridian  and  a  hypermetropia  of  .75  D.  in 
the  150th  meridian.  The  correcting  lens  would  be  +  .25  D.  sph. 
.50  D.  cyl.  axis  60°,  which  could  be  transposed  to  +  .75  D.  sph. 
C    -  .50  D.  cyl.  axis  150°. 


Change  the  retinoscopic  findings  -\-  2.50  D.  in  the  15th  meridian 
at  40  inches,  and  +  3.50  D.  in  the  105th  meridian  at  32  inches  to 
the  proper  sphero  cylinder  for  distant  vision? 

For  the  15th  meridian  after  making  an  allowance  of  1  D. 
for  the  40  inches,  the  refraction  would  be  1.50  D.  hypermetropia; 
and  for  the  105th  meridian  after  making  an  allowance  of  1.25  D. 
for  the  32  inches,  the  refraction  would  be  2.25  D.  hypermetropia. 
The  lens  thus  indicated  would  be  +  1.50  D.  cyl.  axis  105°  C 
+  2.25  D.  cyl.  axis  15°,  or  +  1.50  D.  S.  C  +  -75  D.  cyl.  axis  15°. 


A  toric  lens  used  for  distance  measures  on  its  convex  surface  +  8 
D.  and  on  the  concave  surface  it  shows  in  the  30th  meridian  —  4.75 
D.  and  in  the  120th  meridian  —  4.25  D.  To  what  retinoscopic  find- 
ings at  40  inches  does  this  correspond? 


Fig.  34 


312 


State  Board  Examinations 


A  glance  at  the  diagram  shows  that  this  toric  lens  has  a  power 
of  +  3.25  D.  in  the  30th  meridian  and  of  +  3.75  D.  in  the  120th 
meridian.  Assuming  that  the  retinoscope  had  been  used  at  the 
customary  distance  of  one  meter  for  which  an  allowance  of  1  D. 
had  been  made,  we  must  now  add  this  same  1  D.,  which  would 
make  the  retinoscopic  findings  +  4.25  D.  in  the  30th  meridian 
and  +  4.75  D.  in  the  120th  meridian. 


With  -{-2D.  the  point  oj  reversal  for  the  90  th  meridian  is  at 
40  inches,  and  for  the  180th  meridian  32  inches;  what  would  be  the 
full  correction  for  distance? 

For  the  90th  meridian  after  making  allowance  of  1  D.  for  the 
40  inches  distance,  the  correction  is  +  1  D.,  and  for  the  180th 
meridian  after  making  allowance  of  1.25  D.  for  the  32  inches  dis- 
tance, the  correction  is  +  .75  D. 

This  would  call  for  +  .75  D.  cyl.  axis  90°  C  +  1  D.  cyl. 
axis  180°  which  is  transposed  to  this  sphere  cylinder: 

+  .75  D.  S.  C  +  .25  D.  cyl.  axis  180°. 


A  certain  prescription  is  -{-  2  D.  'C^  +  1.25  cyl.  axis  180°. 
Working  with  the  retinoscope  at  32  inches,  where  will  the  point  of 
reversal  he  for  both  meridians? 


+  2. 
+  1.25 

+  3.25 

+  2. 

+  3.25 

+  1.25 

+  4.50 

+  2. 

+  1.25 

+  3.25 

Retinoscopic  findings 

Fig 

.  36 

Sphero  cyl.  powers 

Fig.  35 


The  first  diagram  shows  that  the  sphero  cylinder  has  a  power 
of  +  2  D.  horizontally  and  of  +  3.25  D.  vertically.  And  inasmuch 
as  we  must  add  1.25  D.  for  the  32  inch  working  distance,  the 
neutralizing  lens  would  be  +  3.25  D.  for  horizontal  meridian  and 
+  4.50  D.  for  vertical  meridian. 


Retinoscopy 


313 


The  reversal  point  of  a  certain  eye  is  for  the  90th  meridian  at 
40  inches  ivhen  a  +  1.25  D.  lens  is  used;  for  the  180th  meridian 
testing  at  the  same  distance  a  +  .75  D.  is  required.  If  a  toric  Jens  is 
prescribed,  and  on  test  with  the  lens  measure  one  surface  is  found  to 
be  —  6  D.  sphere,  and  the  opposite  surface  to  show  +  6.25  D.  in 
the  180th  meridian  and  +  5.75  D.  in  the  90th  meridian,  has  the 
prescription  been  properly  filled? 

After  making  the  usual  addition  of  —  1  D.,  we  find  the 
refraction  of  the  vertical  meridian  to  be  +  -25  D.,  and  of  the 
horizontal  meridian  to  be  —.25  D.,  as  shown  in  first  diagram; 


+  .25 


-  .25 


Retinoscopic  result 

Fig.  3  7 


-  6. 

+  5.75 


.25 


-  6. 
+  6.25 
+  .25 


Toric  lens  powers 

Fig.  38 


An  analysis  of  the  toric  lens  shows  —  .25  D.  power  vertically 
and  +  .25  D.  power  horizontally  as  per  the  second  diagram. 

A  comparison  of  the  two  diagrams  makes  evident  that  the 
prescription  has  not  been  properly  filled,  but  that  the  meridians 
have  been  reversed. 


With  a-\-  1  D.  lens  before  a  certain  eye  the  point  of  reversal  for 
the  90th  meridian  is  at  53  inches,  and  the  point  of  reversal  for  the 
180th  meridia7i  is  at  32  inches.  What  sphero  cylinder  will  give  full 
correction  for  distance? 

Adding  —  .75  D.  for  the  working  distance  of  53  inches,  the 
correcting  lens  for  the  90th  meridian  is  +  .25  D.  And  adding 
—  1.25  D.  for  the  working  distance  of  32  inches,  the  correcting 
lens  for  the  180th  meridian  is  —  .25  D.  This  would  call  for  +  .25 
D.  cyl.  axis  180°  O  —  .25  D.  cyl.  axis  90°,  which  is  transposable 
to  the  following  sphero  cylinder:  +  .25  D.  sphere  O  —  -50  D. 
cvl.  axis  90°. 


314  State  Board  Examinations 

Can  retinoscopy  be  practiced  icith  the  ophthalmoscope? 

Yes,  it  can,  but  the  ophthalmoscopic  mirror  is  concave,  while 
a  plane  mirror  is  preferred. 


If  a  prescription  calls  for  -\-  1  D.  cyl.  axis  90°,  surface  ?iext  to 
the  eye  to  be  deep  concave,  what  kind  of  a  lens  would  have  to  be  made? 

A  toric  lens,  which  is  built  up  from  a  base  curv^e  of  6  D.  on  the 
toric  surface.  The  outside  surface  of  such  lens  would  show  a  +  6 
D.  curve  in  the  90th  meridian  and  a  +  7  D.  curve  in  the  180th 
meridian,  while  the  deep  concave  surface  towards  the  eye  would 
be  —  6  D.  

Is  it  true  as  claimed  that  retinoscopy  is  best  done  with  a  plane 
mirror,  and  what  is  the  reason? 

Retinoscopy  can  be  done  with  either  the  plane  or  concave 
mirror,  but  the  plane  is  preferred,  because  in  its  use  the  distance 
at  which  the  test  is  made  need  not  be  considered,  where  with  the 
concave  mirror  care  must  be  taken  to  keep  beyond  the  focal  dis- 
tance of  the  mirror. 


With  a  plane  mirror  at  20  inches  in  the  usual  static  method  of 
retinoscopy,  a  -\-  1  D.  sphere  neutralizes  motion  in  all  meridians; 
what  is  the  full  correction  for  distance? 

In  working  at  the  customary  distance  of  one  meter,  an  allow- 
ance of  1  D.  is  made:  so  in  working  at  20  inches  an  allowance  of 
2  D.  must  be  made. 

We,  therefore,  add  —  2  D.  to  +  1  D.  and  the  results  is 
—  ID.,  which  would  be  the  full  correction  for  distance. 


In  a  certain  person  the  error  of  refraction  is  corrected  by  the 
following  formula:  +  0.50  D.  S.  —  -\-  1  D.  cyl  axis  45°.  In  the  use 
of  the  retinoscope  with  the  usual  static  method,  what  will  be  the  move- 
merits  of  the  fundus  reflex  at  a  distance  of  one  meter  without  lenses? 

This  formula  would  indicate  that  the  condition  of  the  refrac- 
tion was  hypermetropic,  one  meridian  to  a  greater  extent  than 
the  other,  and  that  therefore  the  emerging  rays  would  be  diver- 


Retinoscopy  315 

gent  and  would  not  meet  in  a  focus ;  as  a  result  of  which  there  would 
be  no  neutral  point  between  the  eye  under  examination  and  the 
observer.  Hence,  the  movement  of  the  reflex  in  the  pupil  with  the 
plane  retinoscope  at  a  distance  of  forty  inches  and  without  any 
lenses  before  the  patient's  eye,  would  be  with.  If  a  concave  mirror 
was  used  the  movement  would  be  aminst. 


What  are  the  optical  principles  of  retinoscopy  with  a  plane 
mirror? 

In  retinoscopy  the  observer  directs  his  attention  to  the  move- 
ments of  the  shadowy  edge  of  an  aerial  image  of  a  bright  spot 
formed  from  the  light  thrown  by  a  mirror  on  the  fundus  of  the 
observed  eye,  as  it  appears  to  pass  across  its  pupil. 

The  direction  of  the  movement  in  the  pupil  of  the  observed 
eye  as  it  appears  to  the  observing  eye,  will  depend  upon  the  posi- 
tion of  the  latter  relative  to  the  image  formed  at  the  conjugate 
focus  of  the  fundus  of  the  observed  eye.  Or  in  other  words 
whether  the  observer  receives  rays  which  come  from  an  aerial 
image  of  the  bright  spot,  or  the  rays  which  proceed  from  the  bright 
spot  itself,  before  they  have  been  united  to  form  an  image. 

In  this  latter  condition  where  the  conjugate  focus  would  fall 
behind  the  nodal  point  of  the  observing  eye,  the  movements  are 
always  in  the  same  direction  as  the  mirror  rotation,  just  as  the 
retina  of  the  eye  would  perceive  the  motion  of  any  object  in  front 
of  it. 

But  when  the  emerging  rays  from  the  observed  eye  are 
brought  to  a  focus  in  front  of  the  observing  eye,  the  movement  in 
the  pupil  will  always  be  in  a  direction  opposite  to  that  of  the  mirror 
rotation. 

If  the  observer  places  his  eye  in  such  a  position  that  the  conju- 
gate focus  of  the  observed  eye  falls  upon  it,  no  mo\'ement  will  be 
apparent. 

In  determining  the  refraction  of  an  eye  by  retinoscopy,  we 
find  that  the  far  point  of  the  eye  or  the  conjugate  focus  of  its 
fundus,  which  we  can  do  by  artificially  bringing  the  far  point  to 
any  derived  finite  distance  by  means  of  a  lens  placed  in  front  of 
the  eye. 

In  myopia  of  1  D.  the  fixed  far  point  is  at  one  meter,  which  is 
the  position  of  the  observing  eye.  The  far  point  of  any  eye  can 


M6  Slate  Board  Examinations 

be  brought  to  the  same  j^oint  of  re\ersal  by  the  proper  lens  placed 
in  front  of  it. 

The  difference  between  the  actual  far  point  and  1  D.  of  my- 
opia, is  represented  by  the  lens  that  was  found  necessary  to  bring 
the  rays  to  a  far  point  at  one  meter.  Therefore,  the  far  point  is 
expressed  by  the  difference  between  the  number  of  the  lens 
employed  and  1  D. 

In  other  word  we  add  —  1  D.  to  the  neutralizing  lens.  For 
example  if  +  1  D.  was  found  necessary  for  neutralization,  then 
+  1  D.  —  1  D.  =  0  or  emmetropia. 

If  neutralizing  lens  was  +  .50  D.  then  +  -^O  D.  —  1  D.  = 
.50  D.  or  half  diopter  of  myopia. 

If  the  neutralizing  lens  was  —  2D.  then  —  2  D.  —  1  D.  = 
—  3  D.  or  three  diopters  of  myopia. 

The  accommodation  of  the  observed  eye  should  be  passive, 
as  otherwise  it  is  impossible  to  measure  its  static  refraction. 

But  accommodation  on  the  part  of  the  observing  eye  need 
not  be  taken  account  of,  as  its  use  or  non-use  cannot  change  the 
result. 

A  patient  has  2  D.  of  myopic  astigmatism.  If  a  -\-  2  D.  sphere 
he  placed  before  the  eye,  where  will  the  point  of  reversal  he  for  the 
horizontal  meridian  if  the  cylinder  required  to  correct  the  error  must 
he  placed  axis  vertical? 

If  the  error  of  refraction  is  simple  myopic  astigmatism,  which 
is  corrected  by  a  —  2  D.  cyl.  axis  90°,  we  know  the  vertical 
meridian  of  the  patient's  eye  is  emmetropic,  and  the  horizontal 
meridian  myopic  to  the  extent  of  2  D. 

When  a  +  2  D.  sphere  is  placed  before  such  an  eye,  the  emme- 
tropic vertical  meridian  will  be  made  artifically  myopic  to  the 
extent  of  2  D.  and  the  point  of  reversal  will  be  20  inches. 

At  the  same  time  the  natural  myopia  of  the  horizontal 
meridian  will  be  artificially  increased  to  4  D.  in  which  case  the 
point  of  reversal  will  be  at  10  inches. 


Using  the  retinoscope  at  40  inches  with  a  -\-  1  D.  sphere  hefore 
the  eye  heing  examined,  the  horizontal  meridian  shon's  7ieutrality. 
When  the  -\-  1  D.  sphere  is  removed,  the  vertical  meridian  shows 
neutrality.    What  is  the  error  of  refraction? 


Retinoscopy  317 

In  working  with  the  retinoscope  at  40  inches,  if  a  +  1  D.  lens 
neutralizes  the  mo\"ement,  emmetropia  is  indicated ;  therefore,  in 
this  case  we  must  assume  that  the  horizontal  meridian  is  emme- 
tropic. 

When  neutrality  of  movement  occurs  naturally  without  the 
intervention  of  any  lens,  myopia  is  indicated,  the  amount  of 
which  would  correspond  to  the  distance  of  the  neutral  point.  In 
working  at  40  inches,  neutrality  of  movement  would  indicate 
myopia  of  1  D.,  and  therefore,  in  this  case  the  vertical  meridian 
is  myopic  1  D. 

If,  then,  the  horizontal  meridian  is  emmetropic,  and  the  ver- 
tical meridian  m\'opic  ID.,  the  error  of  refraction  is  simple  myopic 
astigmatism,  and  the  correcting  lens  would  be  —  1  D.  cyl.  axis 
180°,  which  corresponds  to  astigmatism  with  the  rule. 


Physiology  of  Vision 

What  prevents  an  excessive  amount  of  light  from  entering  the 


eyef 


It  is  the  function  of  the  iris  to  regulate  the  amount  of  Hght 
entering  the  eye,  owing  to  the  fact  that  exposure  to  Hght  causes 
the  circular  fibers  of  the  iris  to  contract  and  as  the  light  increases 
in  intensity  the  pupil  assumes  its  smallest  possible  size,  this  con- 
traction being  the  greatest  when  the  light  falls  upon  the  macula. 


At  zvhat  age  is  the  pupil  of  the  eye  the  largest? 

The  size  of  the  pupil  is  influenced  by  age,  the  color  of  the  iris 
and  the  character  of  the  refraction.  Other  things  being  equal  the 
pupil  is  apt  to  be  larger  in  youth,  in  dark  eyes  and  in  myopic  eyes. 
The  average  diameter  of  the  pupil  is  about  4  mm.  and  while  we 
expect  them  to  be  of  the  same  size  in  the  same  individual,  yet 
slight  differences  in  the  width  of  pupils  are  not  incompatible  with 
health. 

State  the  character  of  the  retina.  Give  the  relation  of  the  retina 
to  the  optic  nerve. 

The  retina  is  a  continuation  or  expansion  of  the  optic  nerve. 
It  is  the  nervous  and  percipient  coat  of  the  eye,  and  is  intended  to 
receive  the  images  of  external  objects  and  transmit  them  to  the 
brain.  It  is  most  sensitive  in  the  region  of  the  macula,  and  least 
sensitive  near  the  ora  serrata.  It  is  transparent  and  hence  invisi- 
ble in  health. 

Describe  a  normal  fundus. 

The  fundus  is  reddish  in  color,  due  to  the  choroid  coat. 

The  optic  disk  is  the  most  prominent  feature  of  the  fundus. 
It  is  about  1.5  mm.  in  diameter  and  is  situated  inwards  from  the 
posterior  pole  of  the  eye.  It  may  be  round,  but  is  usually  slightly 
oval  vertically. 

318 


Physiology  of  Vision  319 

The  central  artery  of  the  retina  and  its  vein  pass  through  the 
axis  of  the  optic  nerve.  Near  the  center  of  the  disk  is  usually  seen 
a  depression  known  as  the  physiologic  cup. 

The  scleral  and  choroidal  rings  may  be  seen  around  the  disk 
of  light  and  dark  color  respectively. 

The  color  of  the  disk  is  pinkish  and  distinctly  lighter  than 
the  surrounding  fundus.  The  veins  are  recognized  by  being  larger 
in  size  and  darker  in  color  than  the  arteries. 

The  macula  lutea  is  situated  on  the  temporal  side  of  the  disk. 
It  is  oval  in  shape  with  its  long  diameter  horizontal  and  it  is 
darker  in  color  than  the  rest  of  the  fundus.  At  its  center  is  the 
fovea  centralis,  which  gives  a  reflex  and  appears  as  a  bright  spot. 


Differentiate  between  the  range  and  the  power  of  accommodation. 

The  range  of  accommodation  is  the  distance  between  the 
near  point  and  the  far  point  while  the  power  of  accommodation  is 
the  force  which  the  ciliary  muscle  is  able  to  exert  to  adapt 
vision  for  the  near  point. 

What  is  accommodation  and  how  is  it  produced? 

Accommodation  is  the  change  in  the  dioptric  condition  of  the 
eye  whereby  it  is  adapted  for  the  perception  of  objects  close  at 
hand.  The  formation  of  a  perfect  image  upon  the  retina  depends 
upon  the  dioptric  apparatus  of  the  eye  being  so  adjusted  that  the 
rays,  diverging  from  any  particular  point,  shall  be  brought  to  a 
focus  and  form  an  image  upon  the  retina.  For  the  parallel  rays 
proceeding  from  objects  at  a  distance,  the  static  refraction  of  the 
eye  sufifices.  From  objects  closer  than  twenty  feet,  the  rays  are 
divergent,  the  amount  of  the  divergence  increasing  with  the  near- 
ness of  the  object,  and  now  the  static  refraction  is  insufficient  to 
form  a  clear  image,  and  the  dynamic  refraction  is  brought  into 
play  by  means  of  the  accommodation,  and  for  each  different  dis- 
tance there  must  be  a  change  in  the  accommodation,  increasing 
as  the  object  approaches  and  diminishing  as  the  object  recedes. 


What  is  amplitude  of  accommodation? 

This  is  the  power  of  accommodation  which  the  eye  is  able 
to  exert  and  represents  the  difference  in  the  dioptric  power  of 


320  State  Board  Examinations 

the  eye  when  the  accommodation  is  passive  and  when  at  its 
maximum  activity,  or  the  difference  between  the  static  and  the 
dynamic  refraction  of  the  eye.  The  ampHtude  of  accommodation 
is  greatest  in  youth  and  gradually  diminishes  with  age,  until  at 
se\enty  years  of  age  it  is  entirely  lost.  About  middle  life  this 
amplitude  is  so  impaired  that  near  vision  is  very  much  interfered 
with;  this  condition  of  presbyopia  calls  for  the  assistance  of  a 
con\ex  lens  to  supply  the  deficiency. 


What  is  convergence?  By  what  means  is  it  obtained? 

Convergence  is  the  act  of  directing  the  visual  axes  of  the  two 
eyes  to  the  same  point  at  some  near  distance,  in  order  that  the 
images  formed  in  the  eyes  shall  be  caused  to  fall  on  the  macula 
of  each  and  be  fused  so  that  one  object  is  seen,  instead  of  two. 
Double  vision  results  when  the  image  falls  upon  parts  of  the  two 
retinae  which  do  not  exactly  correspond.  The  nearer  an  object 
approaches  the  eyes,  the  more  strongly  they  must  be  converged, 
while  at  great  distances  the  need  of  convergence  diminishes  cor- 
respondingly. 

The  function  of  convergence  is  accomplished  by  means  of 
the  internal  recti  muscles,  which  are  also  known  as  the  muscles 
of  convergence. 

What  constitutes  the  amplitude  of  convergence? 

The  amplitude  of  convergence  is  the  power  of  convergence, 
or  the  whole  amount  that  can  be  produced  by  the  strongest  effort 
of  the  internal  recti  muscles,  and  it  is  usually  expressed  in  meter 
angles.  At  extreme  distances  the  visual  lines  are  assumed  to  be 
parallel ;  when  the  eyes  are  directed  to  an  object  one  meter  away, 
the  visual  lines  must  converge  to  this  point,  thus  forming  the 
meter  angle,  which  in  this  case,  equals  one  and  may  be  expressed 
as  follows:  C  =  1  (the  C  being  the  sign  for  amplitude  of  conver- 
gence.) 

If  the  object  looked  at  be  situated  at  half  a  meter,  the  angle 
will  be  twice  as  great,  and  then  C  =  2.  If  situated  at  one-third 
of  a  meter,  the  angle  of  convergence  is  correspondingly  increased, 
and  then  C  =  3.  If  the  object  is  removed  two  meters  or  four 
meters,  the  angle  is  diminished  in  proportion,  and  then  C  =  1/2 
or  C  =  1,4. 


Physiology  of  Vision  321 

What  is  the  visual  field?    The  visual  line? 

The  visual  field  is  the  circular  space  in  front  of  each  eye, 
within  which  objects  are  distinctly  perceptible  while  the  eye  is  in 
a  fixed  position.  In  some  of  the  lower  animals,  on  account  of  the 
position  of  the  eyes,  the  field  of  vision  is  a  complete  sphere,  objects 
being  visible  in  every  direction.  In  man  the  field  is  limited,  and 
yet  it  amounts  to  almost  180°  because  if  the  object  is  brilliant  and 
placed  laterally  at  the  external  borders  of  the  field,  it  does  not 
escape  perception. 

Within  this  field,  however,  there  is  only  one  point  where 
objects  can  be  seen  with  perfect  distinctness,  and  that  is  in  the 
center  of  the  field,  and  its  prolongation  forward  from  the  pupil 
is  known  as  the  "line  of  direct  vision." 

The  limitation  of  distinct  sight  to  the  line  of  direct  vision  is 
practically  compensated  for  by  the  great  mobility  of  the  eyeball, 
which  rapidly  turns  in  all  directions,  shifting  the  line  of  vision  and 
examining,  in  turn,  every  part  of  the  field  of  vision. 


What  is  meant  hy  binocular  vision? 

When  the  two  eyes  are  directed  to  an  object,  an  image  is 
formed  in  each  and  the  function  of  convergence  which  presides 
over  this  department  of  vision  so  directs  the  visual  axes  of  the 
two  eyes  that  the  image  is  formed  on  the  macula  of  each  eye  or, 
at  least,  on  "corresponding  portions"  of  each  retina.  The  impres- 
sion is  carried  to  the  brain  by  each  optic  nerve,  but  as  the  images 
are  exactly  alike  and  are  formed  on  parts  of  the  two  retinae  that 
correspond,  they  are  so  combined  by  the  brain  as  to  give  the 
impression  of  a  single  object.  This  simultaneous  use  of  both  eyes, 
resulting  in  the  production  of  single  vision,  is  known  as  binocular 
vision,  which  may  be  briefly  defined  as  single  vision  with  two  eyes. 


_^    What  is  the  function  of  the  choroid? 

The  choroid  is  the  vascular  coat  of  the  eye  and  consists  of 
connective  tissue  stroma  which  supports  the  numerous  blood- 
vessels, the  larger  of  which  are  in  the  outer  layer,  while  the  inner 
layer  is  devoted  to  the  capillary  network.  Therefore,  the  choroid 
is  to  be  considered  the  chief  nutritive  apparatus  of  the  eye,  be- 


322  State  Board  Examinations 

cause  the  percipient  layers  of  the  retina  and  the  ciHary  muscle, 
which  are  the  most  active  portions  of  the  organ  of  vision,  receive 
their  nutrition  from  this  source.  It  also  contains  pigment  matter, 
which  protects  the  eye  from  excessive  light. 


In  what  way  are  sight  impressions  received  ajid  conveyed  to 
the  braifi? 

A  light  wave  starts  on  its  journey  from  the  luminous  object 
from  which  it  originates.  After  undergoing  the  proper  refraction, 
the  first  actual  step  towards  becoming  a  visual  impulse  is  taken 
when  it  decomposes  the  photo-chemical  substances  of  the  retina 
and  sets  up  vibrations  in  the  extreme  periphery  of  the  end  organs 
of  this  membrane. 

The  excitation  received  by  the  retina  is  then  conveyed  by 
fibers  of  the  optic  nerve  back  to  centers  at  the  base  of  the  brain 
and  thence  to  the  visual  cortex,  which  is  that  part  of  the  con- 
voluted cerebral  surface  concerned  with  the  function  of  sight.  The 
result  in  the  cortical  centers  receiving  the  impulse  is  a  visual 
sensation  or  perception. 


Why  is  it  necessary  for  the  aqueous  humor  to  he  thinner  than 
the  vitreous,  and  yet  it  has  the  same  density? 

These  two  humors  have  practically  the  same  index  of  refrac- 
tion, viz.,  1.33,  but  they  do  not  have  the  same  consistency,  the 
aqueous  being  quite  thin  and  watery,  while  the  vitreous  is  semi- 
fluid, gelatinous  or  jelly-like.  One  reason  why  the  aqueous  should 
be  thinner  is  that  the  movements  of  the  iris  may  quickly  take 
place,  with  nothing  to  retard  them,  as  would  be  the  case  if  the 
humor  in  which  they  floated  was  thicker. 


Why  are  accommodation  and  convergence  closely  related? 

The  purpose  of  the  latter  is  to  form  a  clear  image  upon  the 
retina,  while  the  former  directs  the  tw^o  eyes  to  the  same  point,  so 
that  the  image  may  fall  upon  the  macula  of  each  eye,  in  order  that 
single  binocular  vision  may  result.  For  every  diopter  of  accom- 
modation there  is  a  corresponding  meter  angle  of  convergence  for 


Physiology  of  Vision  323 

each  eye.  In  order  that  this  relation  may  be  maintained,  nature 
has  very  properly  provided  that  the  ciliary  muscle  and  the.  inter- 
nal recti  muscles  shall  be  supplied  by  the  same  nerve,  the  third 
cranial  or  oculo-motor  nerve.  As  the  years  pass  the  habits  formed 
by  the  accommodation  and  convergence  become  more  and  more 
fixed  and  the  relationship  made  still  closer.  This  association  of 
these  two  functions  is  not  the  same  in  all  people,  and  as  the  pres- 
byopic period  gradually  approaches  new  relations  must  be  formed. 


What  influence  has  the  age  upon  the  accommodation? 

The  accommodation  depends  principally  upon  two  factors  — 
the  contractility  of  the  ciliary  muscle  and  the  elasticity  of  the 
crystalline  lens.  As  age  advances  the  ciliary  muscle  gradually 
loses  its  power  of  contractility  and  the  lens  its  power  of  elas- 
ticity. These  two  changes,  the  loss  of  strength  of  the  muscle, 
and  particularly  the  increasing  hardness  of  the  lens,  have  neces- 
sarily a  restricting  influence  upon  the  accommodation.  The  in- 
crease in  the  density  of  the  lens  makes  it  more  difficult  to  be  acted 
upon  by  the  muscle  for  a  change  of  curvature,  even  though  the 
latter  retained  all  of  its  primary  strength. 

The  effect  of  age  upon  the  accommodation  is  modified  by  the 
condition  of  the  refraction  of  the  eye ;  in  hypermetropia  the  lessen- 
ing of  accommodative  power  is  intensified  and  made  manifest 
earlier,  whereas  in  myopia  the  accommodation  is  less  impaired 
and,  then,  not  so  early  in  life. 


What  is  the  function  of  the  eye-lashes? 

When  the  lids  are  partly  closed  the  lashes  come  together  in 
such  a  way  as  to  form  a  kind  of  screen,  which,  while  not  excluding 
vision,  serves  as  a  protection  against  wind  and  dust  and  light  and 
all  foreign  bodies  floating  in  the  air. 


In  what  ivay  do  they  differ  from  ordinary  hairy  growths? 

Their  bulbs  are  freely  supplied  with  nerves,  giving  them  tac- 
tile sensibility,  so  that  they  are  enabled  to  act  as  "feelers"  to 
warn  the  eye  and  reflexly  cause  the  lids  to  close  tightly  on  the 


324  State  Board  Examinations 

approach  of  any  small  object,  as  an  insect  in  the  dark  or  when  the 
vision  is  not  on  guard. 


What  arrangement  is  there  on  the  posterior  surface  of  the  iris 
to  prevent  the  transmission  of  light? 

A  pigment  layer  covering  the  posterior  surface  of  the  iris  as 
far  as  the  anterior  margin  of  the  pupil. 


In  what  way  do  the  nerve  filaments  end  in  the  retina? 
In  the  layer  of  rods  and  cones. 


Which  of  these  is  most  highly  developed  in  man? 
The  rods,  which  are  also  by  far  the  most  numerous. 


Which  are  most  numerous  of  the  macula  lutea  ? 

The  cones;  in  the  fovea  centralis  they  alone  are  present. 


What  are  entoptic  images? 

The  word  "entoptic"  is  derived  from  the  Greek  and  means 
within  the  eye.  These  images  depend  upon  the  presence  of  some 
opacity  in  the  transparent  media  of  the  eye,  such  as  muscae 
volitantes.  They  are  to  be  found  in  all  eyes  to  a  certain  extent, 
and  are  made  more  evident  when  looking  at  a  white  cloud  or  any 
light-colored  object,  especially  through  a  pin  hole. 


What  is  meant  by  intraocular  pressure? 

The  tension  to  which  the  coats  of  the  eye  are  put  by  the 
varying  quantity  of  the  humors  of  the  eye.  When  the  tension  is 
abnormally  increased,  the  condition  is  known  as  glaucoma,  a 
disease  that  is  often  fatal  to  vision. 


What  is  the  visual  purple? 


Physiology  of  Vision  325 

A  certain  coloring  substance  of  the  retina  found  in  the  exter- 
nal segments  of  the  rods,  the  color  being  uniformly  distributed 
throughout  this  portion  of  the  rod,  while  it  is  absent  from  the 
cones  and  the  macula  lutea,  and  hence  it  cannot  be  considered 
essential  to  the  act  of  vision.  But  it  undergoes  changes  when 
exposed  to  light  and,  therefore,  it  is  probable  that  it  plays  some 
important  role  in  the  visual  process.  The  visual  purple  disappears 
when  the  eye  is  exposed  to  light  and  is  restored  when  the  light  is 
excluded.  It  can  be  seen  by  the  naked  eye  or  the  microscope  under 
the  light  of  a  sodium  flame  in  the  fresh  retinae  of  animals  which 
have  been  kept  for  an  hour  or  two  in  the  dark.  When  light  acts 
upon  the  visual  purple,  it  first  produces  visual  yellow  and  then 
visual  white  which  latter  is  described  by  scientists  as  a  greenish, 
fluorescent  substance. 


^^    What  relation  does  the  convergence  of  the  eyes  bear  to  the  accom- 
modation?   Explain  fully. 

In  the  normal  eye  the  relation  between  convergence  and  ac- 
commodation is  very  close.  For  every  effort  of  one  there  is  a  cor- 
responding effort  of  the  other.  In  emmetropia  at  one  meter  there 
is  required  1  D.  of  accommodation  and  1  meter  angle  of  conver- 
gence for  each  eye;  at  one-half  meter  there  is  required  2  D.  of 
accommodation  and  2  meter  angles  of  convergence  for  each  eye 
and  so  on. 

Although  so  closely  associated,  the  relation  between  accom- 
modation and  convergence  is  not  entirely  rigid;  within  certain 
limits  either  may  be  varied  slightly.  The  accommodation  may  be 
lessened  by  convex  lenses  or  increased  by  concave  lenses,  without 
any  change  in  the  convergence.  This  relative  range  of  accommo- 
dation varies  in  different  individuals,  from  3  D.  in  distant  vision 
of  a  young  emmetrope  to  6  D.  in  near  vision. 

As  the  accommodation  can  be  thus  varied  without  change  of 
the  convergence  so  the  latter  within  certain  limits  can  be  increased 
or  diminished  without  affecting  the  accommodation.  The  conver- 
gence can  be  diminished  by  a  prism,  base  in,  when  the  accom- 
modation is  completely  rela.xed.  It  can  also  be  increased  by 
means  of  prisms,  bases  out,  without  bringing  the  accommoda- 
tion into  action.  This  relative  range  of  accommodation  varies 
in  different  persons  up  to  6  m.  a. 


326  State  Board  Examinations 

The  flexibility  in  the  relation  between  accommodation  and 
convergence  is  of  importance  as  allowing  comfortable  binocular 
vision  in  ametropia  that  would  otherwise  be  impossible. 


What  is  the  effect  of  the  contraction  of  the  radiating  muscles  of 
the  iris? 

Dilate  the  pupil. 


Candle  Flame  Images  in  Eye 

Fig.  39 

What  effect  would  he  produced  by  cutting  (a)  the  superior  oblique 
muscle,  (b)  the  internal  rectus  muscle? 

(a)  The  superior  oblique  muscle  turns  the  eye  downward 
and  outward,  rotating  the  upper  end  of  the  vertical  meridian 
inward,  hence  cutting  of  this  muscle  would  limit  the  movement 
downward  and  outward  with  a  corresponding  strabismus  upward 
and  inward. 

(b)  Cutting  of  the  internal  rectus  muscle  would  cause  limi- 
tations of  the  power  of  adduction,  with  perhaps,  divergent 
strabismus  and  crossed  diplopia. 


Physiology  of  Vision  327 

Hoiv  is  the  tension  of  the  eyeball  regulated? 

The  tension  of  the  eyeball  is  maintained  by  the  secretion  of 
the  aqueous  humor,  and  its  equilibrium  is  regulated  by  the  escape 
of  this  humor  into  the  spaces  of  Fontana,  the  canal  of  Schlemm 
and  the  anterior  ciliary  veins. 


What  effect  would  he- produced  if  the  sixth  nerve  were  severed? 

The  sixth  cranial  nerve  is  called  the  abducens  and  supplies 
the  external  rectus  muscle  of  the  eyeball.  Severence  of  this  nerve 
would  cause  inability  to  turn  the  ball  outwards,  with  perhaps  con- 
vergent strabismus  and  homonymous  diplopia,  which  would  be 
increased  by  looking  toward  this  side  and  diminished  when  look- 
ing toward  the  opposite  side. 


Why  is  the  optic  disk  a  Mind  spot  in  the  eye? 

It  is  insensitive  to  light  because  the  percipient  elements  of 
the  retina  are  lacking  here. 


What  is  emmetropia  and  in  what  way  does  it  differ  from  ame- 
tropia? 

Emmetropia  signifies  an  eye  in  measure,  so  that  parallel  rays 
are  exactly  focused  upon  the  retina  without  any  effort  of  accom- 
modation. 

This  is  in  contrast  with  hypermetropia,  where  the  focus  of 
parallel  rays  is  behind  the  retina  and  with  myopia,  where  it  is 
in  front.  In  simple  astigmatism  the  focus  of  one  meridian  is  on 
the  retina  and  of  the  other  back  or  in  front  of  it.  In  compound 
astigmatism  the  focus  of  both  meridians  is  in  front  or  back  of  the 
retina,  at  varying  degrees. 


What  is  the  range  of  focus  between  an  eye  at  rest  and  one  under 
full  accommodative  power  called? 

The  range  of  accommodation. 


v^28  State  Board  Examinations 

What  is  meant  by  the  term  visual  acuity? 

Sharpness  of  sight  or  the  amount  of  vision  possessed  as  com- 
pared with  a  standard,  and  has  reference  to  the  ability  to  perceive 
and  recognize  form  and  outhne. 


What  is  anisometropia? 

That  condition  in  which  the  refraction  of  the  two  eyes  varies. 


In  high  degrees  of  anisometropia  what  is  the  effect  of  hinocidar 
vision? 

If  the  refractive  difference  is  not  too  great,  or  if  the  patient 
can  equalize  the  refraction  of  the  two  eyes  by  an  unequal  con- 
traction of  the  ciliary  muscles  then  binocular  vision  is  likely  to 
be  present.  But  if  the  difference  is  considerable  and  the  ciliary 
muscles  receive  the  same  amount  of  innervation  so  that  the  rela- 
tive difference  betw^een  the  two  eyes  is  constantly  maintained  the 
retinal  image  in  the  more  defective  eye  is  not  only  dimmer,  but 
of  a  different  size  from  its  fellow  under  which  circumstances  the 
incentive  to  binocular  vision  is  very  much  weakened  and  finally 
lost,  or,  if  binocular  vision  is  maintained,  it  is  at  the  expense  of 
constant  effort.  In  other  cases  of  greater  inequality  of  the  retinal 
images,  the  fusion  sense  is  so  weakened  that  no  effort  is  made  to 
maintain  binocular  vision.  The  imperfect  image  of  the  poorer  eye 
is  ignored  or  suppressed  by  the  brain,  and  then  monocular  vision 
is  said  to  exist. 

What  is  the  yellow  spot  of  the  eye? 

It  is  a  highly  sensitive  area  of  the  retina,  situated  at  the  back 
of  the  eye,  in  the  line  of  the  visual  axis  about  1.5  mm.  to  the  tem- 
poral side  of  the  posterior  pole.  This  area  is  about  2.5  mm.  in 
diameter,  and  is  also  known  as  the  macula  lutea,  or  simply  the 
macula.  But  the  true  macula  is  only  about  1  mm.  in  diameter,  and 
is  the  area  of  most  distinct  vision.  In  the  center  of  the  macula 
is  a  minute  depression  about  .25  mm.  in  diameter,  consisting 
entirely  of  narrow  cones  packed  closely  together,  which  is  called 
the  fovea  centralis  on  account  of  its  position,  and  it  is  here  that 
vision  is  most  acute. 


Physiology  of  Visiojt  329 

What  is  the  cause  of  convergence? 

The  abhorrence  of  diplopia  or  the  desire  implanted  by  Nature 
for  single  vision  and,  as  a  result,  the  innervation  of  the  internal 
recti  muscles,  which  are  the  muscles  concerned  in  the  function  of 
convergence. 

What  is  the  blind  spot  of  the  eye? 

It  is  located  at  the  entrance  of  the  optic  nerve,  where  the 
fibers  pass  through  the  sclerotic  at  the  back  of  the  ball,  about 
2  mm.  to  the  nasal  side  of  the  posterior  pole.  This  optic  nerve 
head,  on  account  of  the  absence  there  of  the  retina  proper,  is 
totally  insensitive  to  light,  and  hence  it  is  known  as  the  blind  spot. 

We  are  not  conscious  of  the  existence  of  this  blind  spot  be- 
cause when  our  eyes  are  directed  toward  an  object  the  image  is 
formed  upon  the  macula,  which  is  in  the  line  of  direct  vision, 
while  the  blind  spot  is  situated  to  the  inner  side  of  this  point. 

When  both  eyes  are  open  an  object  may  be  so  placed  that 
its  image  falls  upon  the  blind  spot  of  one  eye,  but  in  such  case  it 
must  fall  upon  the  macula  of  the  other  eye,  and  hence  the  object 
will  be  distinctly  seen. 

It  is  impossible  that  an  image  should  fall  upon  the  blind  spot 
of  both  eyes  at  the  same  time. 

Even  when  one  eye  only  is  used  this  blind  spot  is  not  notice- 
able because  it  is  located  in  a  part  of  the  field  to  which  our  attention 
is  seldom  directed,  and  where  the  perception  of  objects  is  so 
imperfect  that  the  absence  of  one  of  them  momentarily  is  not 
regarded. 

What  is  the  monocular  field  of  vision? 

With  the  eye  looking  straight  forward  (and  confined  to  one 
eye)  it  is  the  space  within  which  objects  are  visible.  Vision  is  per- 
fect only  at  the  center  in  the  line  of  direct  vision,  and  becomes  less 
distinct  towards  the  periphery  of  the  field. 


Why  is  binocular  field  of  vision  wider  than  the  monocular  kind? 

Because  the  second  eye  gives  all  the  additional  field  on  its 
side,  which  is  not  possible  to  one  eye  on  account  of  the  projection 
of  the  nose. 


330  State  Board  Examinations 

What  is  the  principal  advantage  of  indirect  vision? 

Deprived  of  indirect  vision  would  place  a  man  in  the  position 
of  looking  through  a  long,  narrow  tube,  which  would  allow  of 
seeing  nothing  but  the  object  in  the  line  of  direct  vision.  It 
would  be  impossible  to  see  objects  on  one  side  or  the  other, 
abo\e  or  below,  without  an  incessant  turning  of  the  head.  As 
a  person  walks  across  the  street  looking  straight  ahead  to  the 
opposite  side,  where  he  is  going,  he  is  able  without  turning  his 
head  or  eyes,  to  see  if  any  vehicles  are  approaching  in  either 
direction  or  if  there  are  any  obstructions  or  depressions  in  the 
street  by  means  of  his  indirect  vision,  the  importance  of  which 
can  hardly  be  overestimated,  as  it  enables  the  man  to  avoid 
dangers  which  approach  and  menace  him  from  all  sides. 


What  causes  the  crystalline  lefts  of  the  eye  to  become  more 
convex  when  looking  at  a  near  object? 

The  increase  in  convexity  of  the  crystalline  lens  is  accom- 
plished by  means  of  the  contraction  of  the  ciliary  muscle. 


What  is  diplopia  and  hoiv  does  it  differ  from  heterophoria? 

Heterophoria  is  an  imbalance  of  the  ocular  muscles;  diplopia 
is  double  vision.  The  first  is  a  condition,  the  second,  a  symptom. 
We  may  have  and  usually  do  have  heterophoria  without  diplopia 
because  the  eyes  are  able  to  ov^ercome  the  imbalance,  but  we 
do  not  have  diplopia  without  some  disturbance  of  the  muscular 
equilibrium. 

Heterophoria  must  be  sought  and  discovered  by  the  tests  of 
the  optometrist,  while  diplopia  is  self-evident  to  the  patient 
himself.  Heterophoria  may  be  described  as  a  latent  condition 
while  diplopia  is  always  manifest. 


What  is  the  difference  between  binocular  vision  and  fusion? 

Binocular  vision  is  single  vision  with  two  eyes,  and  depends 
upon  the  blending  in  the  brain  of  the  impressions  that  are  made 
upon  corresponding  parts  of  the  two  retinae.  This  usually 
exists  in  connection  with   fusion,   as  shown  in   the   use  of   the 


Physiology  of  Vision  331 

stereoscope,  where  if  the  pictures  are  separate'd  or  approximated, 
the  eyes  will  follow  them  in  the  interest  of  binocular  vision  in 
the  effort  to  maintain  fusion. 

It  is  conceivable  that  there  may  be  some  cases  of  binocular 
vision  of  such  grade  that  the  two  pictures  of  the  stereoscope  will 
be  united  in  one  only  when  placed  in  certain  relative  positions 
corresponding  to  the  directions  independently  assumed  by  the 
visual  axes,  showing  no  effort  to  produce  or  maintain  fusion  on 
account  of  an  absence  of  desire  for  binocular  vision. 


What  is  binocular  vision? 

Single  vision  with  two  eyes,  for  the  maintenance  of  which 
it  is  necessary  that  the  images  of  the  object  fall  upon  identical 
portions  of  the  two  retinae  in  order  that  they  may  transmit  to 
the  brain  a  single  impression;  or  the  object  must  be  at  the  point 
of  intersection  of  the  two  lines  of  direct  vision. 

Vision  of  one  eye  gives  a  flat  appearance,  while  binocular 
vision  gives  the  impression  of  depth  and  solidity,  as  well  as  a 
more  correct  estimate  of  distance  on  account  of  the  amount  of 
convergence  that  is  brought  into  play. 


Describe  the  mechanism  of  accommodatioyi. 

This  depends  upon  the  elasticity  of  the  crystalline  lens  and 
the  contractility  of  the  ciliary  muscle.  The  latter  has  such 
connections  with  the  former  that  when  the  muscle  contracts 
the  lens  becomes  more  convex,  this  increase  of  convexity  being 
greater  on  its  anterior  surface,  and  when  the  muscle  relaxes  the 
lens  becomes  less  convex.  There  are  two  theories  of  accom- 
modation—Helmholtz's  and  Tscherning's  — but  the  essential 
feature  is  that  accommodation  depends  upon  an  increase  in  the 
convexity  of  the  crystalline  lens  and  is  accomplished  by  the 
contraction  of  the  ciliary  muscle. 


What  is  the  difference  in  meaning  betiveen  amplitude  of  accom- 
modation and  range  of  accommodation? 

The  range  of  accommodation  is  the  distance  between  the 
far  point  and  the  near  point,  and  is  the  distance  over  which  the 


332  State  Board  Examinations 

eye  has  command  by  aid  of  its  accommodation.  The  ampHtude 
of  accommodation  is  the  power  of  accommodation  or  the  force 
necessary  to  change  the  adaptation  of  the  eye  from  its  far  point 
to  its  near  point,  and  it  is  represented  by  the  difference  in  the 
refractive  power  of  the  eye  when  in  a  state  of  complete  rest  and 
when  at  its  maximum  of  accommodation. 


What  is  the  function  of  the  cornea? 

The  function  of  the  cornea  is  two-fold : 

It  is  part  of  the  external  coat,  and  as  it  is  tough  and  unyield- 
ing, it  helps  to  maintain  the  shape  of  the  eyeball  and  protect  its 
contents. 

It  is  also  one  of  the  refracting  media  of  the  eye,  receiving 
the  rays  of  light,  and  by  its  density  and  convexity  converges 
them  towards  the  next  medium. 


What  is  the  function  of  the  iris? 

To  regulate  the  amount  of  light  admitted  to  the  retina.  In 
a  bright  light  the  sphincter  fibers  contract  to  protect  the  eye  from 
the  excess  of  light;  in  a  darkened  room  the  dilator  fibers  contract 
to  allow  the  entrance  of  as  much  as  possible  of  the  insufihcient 
Hght.  

What  is  the  function  of  the  crystalline  lens? 

To  still  further  converge  the  rays  of  light  entering  the  eye, 
and  by  its  varying  convexity  to  focus  them  upon  the  retina  no 
matter  what  the  distance  of  the  object  may  be  from  which  they 
come. 


What  is  the  result  of  the  functioning  of  the  ciliary  muscle? 

An  increase  in  the  convexity  of  the  crystalline  lens  as  in  the 
act  of  accommodation,  so  as  to  adapt  the  eye  for  the  diverging 
rays  proceeding  from  close  objects. 


What  is  the  purpose  of  the  extrinsic  muscles  of  the  eye? 


Physiology  of  Vision  333 

To  turn  the  eyeballs  in  the  various  directions  that  may  be 
necessary  and  for  the  maintenance  of  binocular  vision. 


What  is  the  difference  between  supraduction  and  infradiiction? 
Supraduction  is  a  turning  upward;  infraduction  a  turning 


downward. 


The  crystalline  lens  is  sometimes  called  a  hnmor;  is  this  correct? 

The  e^^eball  is  described  as  being  composed  of  three  coats 
within  which  are  contained  three  humors.  These  humors  are 
the  aqueous,  the  crystalline  and  the  vitreous.  The  crystalline  is 
denser  and  thicker  than  the  other  two  humors,  but  at  the  same 
time  it  is  jelly-like  or  semi-fluid,  so  that  it  is  really  a  humor. 


What  is  the  usual  difference  between  the  pupillary  distance  for 
far  and  that  for  near? 

The  pupillary  distance  for  reading  is  about  four  mm.  (one- 
sixth  of  an  inch)  less  than  for  distance. 


How  can  you  find  the  number  of  degrees  of  convergence  used  at 
the  ordinary  reading  distance? 

The  degree  of  convergence  is  expressed  in  terms  of  the  meter 
angle,  which  is  the  angle  through  which  each  eye  must  turn  from 
parallelism  of  the  visual  lines  so  that  these  lines  may  meet  at  a 
distance  of  one  meter.  The  advantage  of  this  system  is  that  in 
emmetropia  the  meter  angles  of  convergence  are  equal  to  the 
diopters  of  accommodation.  The  objection  to  it  is  that  the  meter 
angle  has  no  fixed  value  on  account  of  the  variation  in  the  inter- 
pupillary  distance,  but  for  the  average  distance  it  is  about  1^°. 
As  the  angle  of  deviation  is  about  one-half  the  refracting  angle  of 
a  prism,  this  would  correspond  to  the  deviation  of  a  3°  prism. 
Therefore,  one  meter  angle  of  convergence  is  equivalent  to  the 
effect  of  a  prism  of  3°  before  each  eye,  or  to  the  effect  of  a  prism  of 
.  6°  before  one  eye. 

At  the  usual  reading  distance  of  13  inches,  where  3  D.  of 
accommodation  is  in  use,  the  equivalent  would  be  9°  before  each 
eye  or  18°  before  one  eye. 


334  State  Board  Examinations 

Which  is  the  stro7iger  function,  accommodation  or  convergence? 
On  what  do  you  base  your  conchision? 

There  may  be  a  difference  of  opinion  on  this  point,  and  it 
probably  varies  in  different  persons  and  at  different  times  of  life. 
There  is  always  an  abhorrence  of  diplopia,  which  is  more  dis- 
turbing than  a  slight  indistinctness  of  vision,  and  would  seem  to 
indicate  that  convergence  was  the  most  important.  But,  on  the 
other  hand,  in  young  hypermetropes  in  order  to  bring  the  accom- 
modation into  play  and  secure  clear  vision  strabismus  and  mo- 
nocular vision  are  established,  which  would  seem  to  indicate  that 
accommodation  was  the  dominant  function. 


What  are  the  two  associated  functions  of  the  eye  as  regards 
changes  of  the  gaze  from  point  to  point,  and  what  is  the  nature  of 
this  association? 

Accommodation  and  convergence,  the  association  between 
which  being  so  close  that  exercise  of  one  of  them  is  involuntarily 
accompanied  by  a  corresponding  action  of  the  other. 


What  stimulus  is  it  that  results  in  exact  binocular  vision? 

The  fusion  sense  or  fusion  faculty,  aided  by  a  strong  natural 
desire  for  single  vision. 


Name  all  of  the  extrinsic  muscles  brought  into  play  in  converging 
to  a  point  eighty  inches  away;  four  inches  away. 

Converging  at  eighty  inches  is  accomplished  mainly  by  the 
internal  recti  muscles.  At  four  inches  these  muscles  are  reinforced 
by  the  superior  and  inferior  recti  muscles. 


When  is  the  punctum  proximum  of  accommodation  and  con- 
vergence at  the  same  point? 

In  emmetropic  and  orthophoric  eyes,  when  the  accommoda- 
tion and  convergence  can  be  used  in  the  same  proportion  and  to 
the  full  extent  to  focus  and  fix  a  near  object. 


Physiology  of  Vision  335 

In  what  way  does  the  vision  of  a  color-blind  person  differ  from 
the  vision  of  a  perso?i  with  itormal  vision? 

Color  blindness  does  not  seem  to  reduce  the  visual  acuity  as 
it  might  be  thought  to  do  at  first  sight,  but  as  a  matter  of  fact  the 
general  vision  of  the  color  blind  is  up  to  the  standard  of  normal 
eyes.  In  those  colors  which  they  cannot  see  as  such  they  can  dis- 
tinguish differences  of  shade  and  tone  that  are  dependent  upon 
the  admixture  of  white,  even  better  than  normal  eyes. 

When  a  totally  color  blind  person  looks  at  a  colored  object  he 
is  conscious  only  of  the  white  light  which  is  present  in  varying  de- 
grees in  every  color,  and  instead  of  color  the  object  presents  shades 
of  gray,  as  in  an  engraving.  In  cases  of  blindness  for  red,  when  a 
red  object  is  looked  at  there  is  no  stimulation  of  the  red  fibers, 
but  there  is  an  impression  of  the  green  fibers,  and  to  a  slight  extent 
of  the  violet.  A  red  object  therefore  makes  the  same  impression 
as  a  green  one,  but  he  is  sometimes  able  to  distinguish  between  the 
two  by  their  difference  in  brilliancy. 


Why  are  we  not  conscious  of  the  existence  of  the  blind  spot  when 
we  close  one  eye? 

Because  it  covers  such  a  small  area,  and  besides  is  located  in 
a  part  of  the  field  of  vision  to  which  our  attention  is  scarcely 
directed,  and  where  the  perception  of  various  objects  is  so  imper- 
fect that  the  momentary  absence  of  one  of  them  is  not  regarded ; 
and  finally  because  the  brain  from  long  experience  has  learned  to 
ignore  it. 

What  is  the  purpose  of  the  iris  of  the  eye  and  to  what  extent  is 
it  effective? 

To  regulate  the  amount  of  light  admitted  to  the  eye.  There 
is  a  limit  to  its  contractibility  in  shutting  out  excessive  light,  as 
there  is  to  its  dilatability  in  admitting  diminished  light. 


What  is  the  difference  in  the  dioptric  power  of  the  eye  between 
when  the  accommodation  is  at  rest  and  in  fidl  force  called? 


336  State  Board  Examinations 

It  is  that  which  is  supplied  by  the  ampHtude  of  accommoda- 
tion, which,  added  to  the  power  of  refraction  of  the  eye  when  in 
repose,  represents  its  full  positive  refracting  power. 


What  effect  does  age  have  on  the  accommodation  and  on  the  con- 
vergence? 

There  is  a  steady  and  gradual  diminution  of  the  power  of 
accommodation  with  the  advance  of  years,  while  the  power  of 
convergence  is  but  little  if  any  affected. 


What  is  meant  by  positive  and  7iegative  convergence,  and  what  is 
the  total  amplitude  of  convergence? 

Positive  convergence  is  the  turning  inward  of  the  visual  lines 
so  that  they  shall  meet  at  the  point  of  fixation. 

Negative  convergence  is  a  divergence  of  the  visual  lines. 

The  total  amplitude  of  convergence  is  represented  by  the 
nearest  point  for  which  the  eyes  can  converge.  If  this  point  was 
5  inches,  it  would  represent  a  converging  power  of  about  8  meter- 
angles. 

What  is  meant  by  the  term  binocular  vision? 
Single  vision  with  two  eyes. 


In  what  way  does  the  human  eye  resemble  a  photographic  camera 
and  in  what  way  is  it  different? 

In  the  human  eye  the  image  is  formed  on  the  retina  by  means 
of  the  crystalline  lens  which  is  adjustable  for  vision  at  different 
distances,  very  much  as  in  the  camera,  the  image  is  formed  on  the 
sensitive  plate  or  film  by  means  of  the  converging  lens,  the  instru- 
ment being  adjustable  for  objects  at  different  distances,  by  alter- 
ing the  distance  between  the  lens  and  the  film,  which  is  capable 
of  receiving  only  one  image,  while  the  capacity  of  the  retina  is 
unlimited. 

Why  does  the  pupil  of  the  eye  look  black  when  it  is  really 
transparent? 


Physiology  of  Vision  337 

Because  there  is  no  intraocular  illumination,  or  no  inside 
light  to  come  out.  If  light  entered  the  eye  from  a  flame,  it 
would  return  in  the  same  direction  from  which  it  came,  and  in 
order  for  the  observer  to  see  it,  he  must  get  in  the  path  of  the 
returning  rays,  and  in  so  doing  his  head  gets  in  the  way  and  shuts 
off  the  entering  light.  This  is  overcome  in  the  ophthalmoscope 
where  the  mirror  acts  as  the  source  of  light,  and  in  returning 
some  of  the  light  passes  through  the  sight  hole"  into  the  eye  of  the 
observer. 


What  is  the  difference  between  monocular  vision,  binocular 
vision  and  the  fusion  sense? 

Monocular  vision  is  one  eye  vision.  In  binocular  vision 
both  eyes  are  used  and  the  image  formed  on  the  macula  of  each, 
but  they  are  blended  in  the  brain  so  that  we  are  conscious  of 
only  one  object. 

The  fusion  sense  may  be  regarded  as  presiding  over  binocular 
vision,  and  is  that  function  of  the  visual  centers  in  the  brain 
that  enables  fusion  of  the  two  images  to  be  made  and  maintained. 


Hoio  is  the  accommodation  of  the  eye  produced  and  why  does 
it  fall  off  with  age? 

The  accommodation  is  produced  by  an  increased  convexity 
of  the  crystalline  lens  and  is  caused  by  contraction  of  the  ciliary 
muscle.  It  lessens  with  age  because  the  crystalline  grows  denser 
and  harder  and  is  not  able  to  respond  so  readily  to  the  action  of 
the  ciliary  muscle. 

What  is  the  range  of  accommodation  in  any  individual,  and 
how'  may  it  be  measured? 

The  writer  regards  the  distance  between  the  near  and  the 
far  points  over  which  the  eye  has  command,  by  the  aid  of  its 
accommodation,  as  the  range  of  accommodation. 

But  the  question  implies  what  the  writer  terms  the  ampli- 
tude of  accommodation,  which  is  the  force  necessary  to  change 
the  eye  in  its  adaptation  from  its  far  point  to  its  near  point  and 
is  represented  by  that  convex  lens  which  would  enable  the  eye 


338  State  Board  Examinations 

to  see  at  its  near  point  when  the  accommodation  is  at  rest.  The 
accommodation  is  therefore  equal  to  a  convex  lens  if  such  strength 
as  will  give  to  rays  proceeding  from  its  near  point  the  same 
direction  as  if  they  come  from  the  far  point.  Hence  we  measure 
the  near  point  and  transpose  into  D's.  As  for  instance  a  near 
point  if  ten  inches  represents  an  accommodation  of  4  D. 


What  is  meant  hy  the  term  spasm  or  cramp  of  the  accommoda- 
TtonK 

A  persistent  contraction  of  the  ciliary  muscle,  which  fails 
to  relax,  even  when  there  is  no  need  for  its  contraction. 


What  is  the  difference  between  subnormal  accommodation  and 
subnormal  range  of  accommodation? 

By  subnormal  accommodation  the  writer  would  understand 
that  the  power  or  amplitude  of  accommodation  was  below  the 
normal  standard  for  that  particular  age. 

By  subnormal  range  of  accommodation  we  would  understand 
that  the  distance  between  near  and  far  points  is  less  than  normal. 


How  close  is  the  relation  between  accommodation  and  conver- 
gence? 

This  relation  is  close  but  not  absolute,  because  although  so 
intimately  connected,  they  may  within  certain  limits  be  used 
independently  of  each  other. 

For  instance,  the  effort  of  accommodation  may  be  increased 
or  diminished  by  the  use  of  concave  or  convex  spheres,  respec- 
tively, while  the  same  degree  of  convergence  is  maintained. 

Or  the  effort  of  convergence  is  lessened  by  prisms  bases  in 
without  a  corresponding  diminution  of  accommodation,  as  shown 
by  the  fact  that  the  distinctness  of  the  object  is  not  impaired. 

Or  the  effort  of  convergence  may  be  increased  by  prisms 
bases  out  without  a  corresponding  increase  of  accommodation, 
as  shown  by  no  interference  with  the  clearness  of  vision. 

But  at  the  same  time  the  general  statement  holds  good  that 
the  functions  are  so  closely  related  that  with  every  effort  of 
accommodation  there  is  a  corresponding  effort  of  convergence. 


Physiology  of  Vision  339 

Why  is  it  that  while  the  orbits  diverge  the  eyes  look  straight 
ahead? 

By  the  action  of  the  extra  ocular  muscles,  and  especially  the 
internal  recti.  These  are  the  strongest  of  all  the  muscles  and 
easily  overcome  the  divergence  of  the  orbits. 


When  is  an  eye  orthophoric? 

When  there  is  no  imbalance  of  the  extra  ocular  muscles. 


What  is  meant  hy  acuity  of  vision  ajid  zvhat  is  the  usual  stand- 
ard of  the  same? 

Acuteness  of  vision  is  a  function  of  the  nervous  system 
of  the  eye;  it  is  for  the  retina  what  tactile  sensibility  is  for  the 
skin,  and  the  two  functions  are  determined  in  a  similar  manner. 
We  seek  in  both  for  the  smallest  distance  between  two  points 
which  can  be  perceived  separately.  For  the  skin,  the  mechanical 
pressure  of  two  points  of  a  compass  is  employed;  while  for  the 
retina  it  depends  upon  the  retinal  images  of  two  luminous  points. 

Visual  acuity  therefore  represents  the  smallest  retinal  image, 
the  form  of  which  can  be  distinguished,  for  which  its  two  points 
must  be  separated  by  a  certain  small  distance,  and  this  distance 
corresponds  in  the  normal  eye  to  a  visual  angle  of  one  minute. 


Why  does  not  the  amplitude  of  the  convergence  fall  off  as  rapidly 
with  age  as  does  the  amplitude  of  the  accommodation? 

It  is  probable  that  all  the  muscles  of  the  body  show  some 
loss  of  power  with  the  advance  of  age,  but  the  more  rapid  loss 
of  accommodation  is  due  rather  to  the  increasing  firmness  of 
the  crystalline  lens  than  to  the  loss  of  power  of  the  ciliary  muscle, 
and  as  a  result  the  former  does  not  respond  to  the  latter.  It  is 
fair  to  conclude  that  the  ciliary  muscle  does  not  weaken  any 
faster  than  the  muscles  of  conv^ergence,  but  the  first  is  no  longer 
able  to  increase  the  convexity  of  a  crystalline  which  has  become 
dense  and  hard,  whereas  the  second  simply  causes  motion  and 
there  is  no  change  occurring  in  the  eye  to  make  that  motion  more 
difficult. 


340  State  Board  Examinations 

What  is  meant  by  the  term  "axis  of  the  eye,''  and  has  the  human 
eye  an  axis? 

The  human  eye  anatomically  speaking  does  not  have  an 
axis,  but  the  term  "axis  of  the  eye"  is  an  imaginary  line  which 
passes  perpendicularly  through  the  center  of  the  cornea,  the 
center  of  the  crystalline  lens  and  the  center  of  the  fundus,  which 
latter  is  a  little  to  the  nasal  side  of  the  macula  lutea.  The  front 
end  of  this  line  at  the  apex  of  the  cornea  is  the  anterior  pole,  and 
the  other  end  at  the  center  of  the  fundus  is  the  posterior  pole. 


What  is  abduction  of  the  eyes  and  ivhen  is  it  exerted  and  by  what 
muscles? 

Abduction  is  turning  of  the  eyes  outwards,  and  takes  place 
when  looking  out  at  distant  objects  after  the  eyes  have  been 
converged  in  near  vision  and  is  effected  by  the  external  recti 
muscles.  It  may  be  considered  a  passive  function,  in  contrast 
with  adduction  which  is  an  active  one. 

When  prisms  are  placed  before  the  eyes  bases  in  abduction 
is  called  into  action  to  prevent  diplopia. 


How  can  one  see  opacities  in  his  own  eyes  if  any  be  present? 

Any  object  in  the  eye  in  front  of  the  sensitive  retina  inter- 
cepts the  light  that  passes  through  the  pupil  and  throws  shadows 
which,  under  certain  conditions,  can  be  perceived.  A  flame  at  a 
distance  of  fifteen  feet  is  looked  at  through  a  strong  convex  lens 
held  two  or  three  inches  from  the  eye,  when  a  bright  patch  of  light 
will  be  seen  formed  by  circles  of  diffusion,  upon  which  the  presence 
of  any  opacities  in  the  eye  becomes  manifest  by  the  shadows  that 
are  thrown  upon  it. 

What  is  the  difference  between!  the  optical  and  visual  axis  of 
the  eye? 

The  optic  axis  is  an  imaginary  line  that  passes  perpendicu- 
larly through  the  center  of  the  cornea,  the  center  of  the  crystalline 
lens  and  the  center  of  the  fundus,  which  point  is  usually  near  the 
inner  margin  of  the  macula. 


Physiology  of  Vision  341 

The  visual  axis  is  an  imaginary  line  that  passes  from  the 
object  looked  at  through  the  nodal  point  to  the  macula. 

It  is  possible  that  the  visual  axis  should  coincide  with  the 
optic  axis,  but  it  seldom  does;  the  two  axes  crossing  and  forming 
at  the  nodal  point  of  the  angle  of  Alpha  or  of  Gamma. 


What  advantage  has  binocular  vision  over  the  monocular  form, 
as  possessed,  for  instance,  by  a  one-eyed  man? 

The  advantages  of  binocular  vision  are  the  power  to  recog- 
nize depth  and  perspective  or  the  appreciation  of  solidity;  and 
the  more  correct  estimation  of  distance  as  indicated  by  the  amount 
of  convergence  necessary. 


What  is  the  blind  spot  and  %vhy  is  it  so  called?  How  may  its 
location  be  detected? 

The  blind  spot  is  at  the  entrance  of  the  optic  nerve,  and  it  is 
so  called  because  of  the  absence  of  the  percipient  layer  of  the  retina 
there.    It  is  insensitive  to  light. 

It  can  be  detected  by  the  following  experiment:  two  black 
spots  on  a  white  card,  left  eye  closed  and  with  right  eye  look  at 
left  hand  spot.  The  card  is  moved  farther  from  or  closer  to  the  eye 
until  a  position  is  found  where  the  right  hand  image  is  lost,  because 
its  image  falls  upon  the  blind  spot.  As  the  position  of  the  card  is 
varied,  the  spot  again  comes  into  view. 


Why  is  the  association  of  accommodation  and  convergence  a 
close  one? 

Because  it  is  necessary  to  use  both  in  equal  proportion  in  near 
vision,  and  because  Nature  made  it  so,  both  functions  being  sup- 
plied by  the  third  cranial  nerve. 


Why  does  the  pupil  look  black  ivhen  it  is  really  transparent? 

Because  of  the  absence  of  intra-ocular  illumination,  and 
because  there  are  no  rays  of  light  passing  from  the  eye  of  the 
patient  to  the  eye  of  the  observer.    Rays  of  light  entering  an  eye 


342  State  Board  Examinations 

are  reflected  back  to  their  source,  and  in  order  to  obtain  an  illu- 
minated pupil  these  returning  rays  must  be  intercepted. 

This  is  accomplished  by  making  a  mirror  the  source  of  light, 
and  as  the  rays  from  the  obser\'ed  eye  return  to  the  mirror,  the 
obser\'er  is  able  to  receive  some  of  these  return  rays  through  the 
opening  in  the  mirror. 


What  is  the  result  of  contraction  of  the  radiating  muscular 
fibers  of  the  iris? 

Dilatation  of  the  pupil. 


Pathological  Conditions 

What  are  the  different  forms  of  color  blindness? 

The  different  forms  of  color  blindness  are  red,  green  and 
violet,  of  which  the  first  two  are  the  most  common. 


How  can  we  tell  whether  there  is  any  sense  of  light  in  a  sus- 
pected case  of  cataract? 

By  means  of  a  lighted  candle  in  a  darkened  room,  and  by  the 
ability  of  the  patient  to  recognize  the  light  and  locate  the  direction 
from  which  it  comes. 

How  can  you  tell  if  a  patient  has  glaucoma  or  not?  What  do  you 
see  with  the  ophthalmoscope  that  will  give  you  this  information? 

By  the  rapid  recession  of  the  near  point,  by  the  increased 
tension  and  stony  hardness  of  the  eyeball,  by  the  subjective 
symptom  of  halo  or  rainbow  around  a  light,  by  severe  neuralgic 
pains  that  are  complained  of,  by  sluggish  or  immobile  pupil,  by 
impairment  of  vision,  by  cloudiness  of  the  aqueous  and  vitreous 
and  cornea,  and  by  contraction  of  the  field  of  vision.  The  ophthal- 
moscope will  show  venous  congestion,  arterial  pulsation  and  cup- 
ping of  the  optic  disk. 

What  is  the  difference  between  an  amblyopic  eye  and  an 
asthenopic  eye? 

In  the  amblyopic  eye  vision  is  impaired  and  no  improvement 
is  afforded  by  glasses.  In  the  asthenopic  eye,  vision  is  usually 
good,  but  the  eyes  can  be  employed  but  little  for  close  work, 
because  all  such  use  of  the  eye  is  attended  with  discomfort  or 
pain.  An  amblyopic  eye  has  blurred  vision,  while  an  asthenopic 
eye  means  weak  sight. 

What  is  meant  by  retinal  fatigue,  and  how  is  its  existence 
generally  proved? 

343 


344  State  Board  Examinations 

This  means  exhaustion  of  the  optic  ner\'e  and  retina,  and 
quickly  comes  on  when  the  eyes  are  steadily  fixed  on  one  object, 
and  manifests  itself  by  impairment  of  vision. 

This  is  brought  home  to  the  optometrist  in  his  daily  work. 
The  patient  is  looking  intently  at  the  test  letters  as  one  lens  after 
another  is  tried ;  he  is  unable  to  decide  which  lens  is  the  better,  in 
fact  he  will  probably  say  he  cannot  see  the  letters  at  all.  A  closing 
of  the  eye  or  turning  in  another  direction  suffices  to  relieve  the 
exhaustion  of  the  retina  and  allows  the  examination  to  proceed. 
The  optometrist  would  do  well  to  take  advantage  of  these  rests 
frequently  during  his  examination. 


What  is  the  effect  on  the  mobility  of  the  eye  if  the  internal  rectus 
is  paralyzed? 

Partial   or   total   loss  of  power   to   turn   eye   inward,    thus 
impairing  the  function  of  convergence. 


Suppose  an  accident  happens  to  the  eye  whereby  some  of  the 
aqueous  humor  and  some  of  the  vitreous  humor  is  lost.  Will  nature 
replace  these  humors? 

The  aqueous  humor  will  be  quickly  replaced,  but  the  vitreous 
never. 

In  color  blindness  of  the  usual  type,  why  does  the  patient  confuse 
shades  of  green  with  shades  of  red? 

According  to  the  Young-Helmholtz  theory  we  have  three 
primary  color  perceptions  corresponding  to  the  three  primary 
colors  of  red,  green  and  violet.  The  absence  or  impairment  of 
one  or  more  of  the  primary  perceptions  constitutes  color  blind- 
ness, as  a  result  of  which  these  colors  are  confused.  These 
color  sensations  are  conveyed  to  the  brain  by  three  sets  of  nerves, 
each  set  conveying  not  only  the  sensation  of  its  special  color, 
but  also  to  a  slight  extent  that  of  the  other  two. 

In  color  blindness  there  is  a  loss  of  sensation  to  one  or  more 
of  the  three  colors,  or  an  impairment  of  one  or  more  of  the  sets 
of  nerves,  which  is  discovered  when  the  patient  is  asked  to  match 
various  colored  skeins  of  varns. 


Pathological  Conditions  345 

What  explanation  can  be  given  for  the  oscillation  of  the  eyes  in 
many  albinos^ 

This  condition,  to  which  the  term  nystagmus  has  been 
given,  is  most  commonly  found  in  persons  with  congenitally 
defective  vision,  among  whom  albinos  are  to  be  classed.  On 
account  of  the  lack  of  pigment  in  the  choroid  and  iris,  there  is 
no  provision  for  modifying  the  brightness  of  the  light,  and  the 
patient  suffers  from  the  dazzling,  and  his  vision  is  impaired. 
Just  how  the  oscillation  is  produced  is  a  disputed  question,  but 
it  is  probable  that  in  these  congenital  cases  the  absence  of  the 
stimulus  which  distinct  retinal  images  cause,  interferes  with  the 
development  and  functioning  of  the  centers  in  the  brain  that 
govern  the  co-ordination  of  the  ocular  muscles. 

It  is  an  interesting  fact  that  in  those  patients  where  the 
nystagmus  is  due  to  a  congenital  defect,  there  is  no  complaint 
of  oscillation  of  objects  looked  at;  whereas,  when  the  affection 
comes  on  later  in  life,  such  patients  are  very  much  annoyed  by 
this  symptom. 


What  is  amblyopia  and  ivhat  are  some  of  the  causes  of  it? 

Amblyopia  is  impaired  vision,  which  is  not  caused  by  an 
error  of  refraction,  but  is  due  to  functional  disturbance  or  disease 
of  some  part  of  the  visual  apparatus,  either  the  retina,  the  optic 
nerve  or  the  brain.  It  sometimes  exists  without  any  evidences 
that  are  visible  to  the  ophthalmoscope. 

Amblyopia  ex  anopsia  is  due  to  non-use  of  one  eye  as  in 
strabismus.  Reflex  amblyopia  to  irritations  in  some  other  part 
of  the  body.  Traumatic  amblyopia  to  injury.  Ursemic  amblyopia 
to  Bright's  disease.  Toxic  amblyopia  to  tobacco  and  alcohol  in 
excess. 

It  may  be  recognized  by  its  inability  to  respond  to  any 
glass  placed  before  the  eye,  and  by  the  failure  of  the  pin  hole  to 
afford  any  improvement  in  vision. 


Why  is  it,  after  the  removal  of  a  cataract,  that  a  strong  glass 
can  be  placed  over  the  aphakic  eye  and  be  worn  with  comfort,  when 
this  cannot  be  done  in  cases  of  high  anisometropia? 


346  State  Board  Examinations 

This  is  possible  only  when  the  other  eye  suffers  with  im- 
paired vision,  probably  from  a  partly  developed  cataract.  Under 
such  conditions  the  burden  of  vision  is  borne  by  the  aphakial  eye 
with  its  proper  correction.  As  long  as  the  vision  of  one  eye  is 
good,  or  at  least  serviceable,  it  is  not  customary  to  perform  a 
cataract  operation  on  the  other  eye,  but  a  time  finally  comes  when 
vision  has  been  so  much  impaired  that  something  must  be  done, 
and  then  the  poorest  eye  is  operated  upon.  If  successful  the 
vision  of  this  eye  with  its  correcting  lens  is  so  much  better  than 
the  other  eye,  that  it  becomes  the  dominant  eye,  and  is  not 
disturbed  by  the  relatively  poorer  vision  of  the  other  eye. 


When  is  detachment  of  the  retina  to  be  suspected? 

The  diagnosis  of  this  condition  can  be  made  only  by  the 
ophthalmoscope.  In  a  partial  detachment  the  normal  reflex  is 
absent  at  the  portion  detached,  and  instead  it  is  grayish  or  whitish 
on  account  of  opacity  of  the  retina.  As  the  detached  portion 
projects  into  the  cavity  of  the  eyeball,  it  can  be  examined  by 
the  direct  method  w^ith  a  convex  lens.  The  gray  reflection  can 
be  seen  to  be  folded,  and  the  few  retinal  vessels  that  pass  over 
it  have  lost  their  light  streak,  appear  dark  in  color  and  pursue  a 
tortuous  course.  When  the  eye  is  quickly  moved  in  different 
directions,  motion  can  be  observed  in  the  folds  depending  upon 
the  amount  of  the  underlying  fluid. 


What  is  the  effect  of  atropine? 

To  suspend  accommodation  and  dilate  the  pupil.  It 
paralyzes  the  peripheral  cells  of  the  third  cranial  nerve  as  supplied 
to  the  ciliary  muscle  and  the  iris,  while  it  stimulates  the  radiating 
muscular  and  sympathetic  fibers  of  the  iris. 


What  is  meant  by  night  blindness? 

This  is  a  well  recognized  symptom  of  the  disease  known  as 
retinitis  pigmentosa.  While  vision  is  never  perfect,  yet  such  a 
patient  can  see  fairly  well  in  bright  daylight,  but  on  a  dull  day 
or  at  twilight  or  by  insufficient  artificial  light,  vision  is  very 


Pathological  Conditions  347 

greatly  impaired.     This  is  said  to  be  due  to  defective  power  of 
adaptation  of  the  retina,  rather  than  to  defective  light  sense. 


What  is  cataract  and  what  is  the  popular  conception  of  it? 

Cataract  is  a  translucent  or  opaque  crystalline  lens.  It  is 
sometimes  spoken  of  as  "on  the  eye,"  when  it  is  confused  with 
an  opacity  of  the  cornea. 


Why  may  a  chalazion  temporarily  change  the  refractive  con- 
dition of  the  eye? 

This  is  a  small  tumor  of  the  lid  and  it  is  possible  that  by 
pressure  on  the  cornea  it  may  so  change  its  curvature  as  to  pro- 
duce a  temporary  condition  of  astigmatism. 


Is  there  a  difference  between  color  blindness  and  color  ignorance? 

Color  blindness  is  a  congenital  condition,  and  is  due  to  the 
absence  or  deficiency  of  one  of  the  retinal  color  elements;  while, 
in  color  ignorance  there  is  an  inability  to  name  colors  because 
of  lack  of  training  or  education  in  them. 


The 

Principles  of  Refraction 

in  the  Human  Eye,  Based  on  the 
Laws  of  Conjugate  Foci 

By  SWAN  M.  BURNETT,  M.D.,  PH.D. 

Formerly  Professor  of  Ophthalmologry  and  Otology  in  the  Georgetown 
University  Medical  School;   Director  of  the  Eye  and  Ear  Clinic, 
Central  Dispensary  and  Emergency  Hospital ;   Ophthalmo- 
logist to  the  Children's  Hospital   and  to  Providence 
Hospital,  etc.,  Washington,  D.  C. 

IN  this  treatise  the  student  is  given  a  condensed  hut 
thorough  grounding  in  the  principles  of  refraction 
according  to  a  method  which  is  both  easy  and  funda- 
mentah  The  few  laws  governing  the  conjugate  foci 
lie  at  the  basis  of  whatever  pertains  to  the  relations  of 
the  object  and  its  image. 

To  bring  all  the  phenomena  manifest  in  the  refraction  of 
the  human  eye  consecutively  under  a  common  explanation  by 
these  simple  laws  is,  we  believe,  here  undertaken  for  the  first 
time.  The  comprehension  of  much  which  has  hitherto  seemed 
difficult  to  the  average  student  has  thus  been  rendered  much 
easier.  This  is  especially  true  of  the  theory  of  Skiascopy, 
which  is  here  elucidated  in  a  manner  much  more  simple  and 
direct  than  by  any  method  hitherto  ofifered. 

The  authorship  is  sufficient  assurance  of  the  thorough- 
ness of  the  work.  Dr.  Burnett  was  recognized  as  one  of  the 
greatest  authorities  on  eye  refraction,  and  this  treatise  may 
be  described  as  the  crystallization  of  his  life-work  in  this  field. 
The  text  is  elucidated  by  24  original  diagrams,  which 
were  executed  by  Chas.  F.  Prentice,  ALE.,  whose  pre-emi- 
nence in  mathematical  optics  is  recognized  by  all  ophthalmol- 
ogists. 

BOUND    IN    SILK    CLOTH 
Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$1.50 

A* 

Published  by 
THE  KEYSTONE   PUBLISHING   COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


The  Optician's  Manual 

Volume  I. 

By  C.  H.  BROWN,  M,  D. 

(jraduate  I'niversity  of    Pennsylvania;    Professor    of    Principles  and 

Practice  of  Optometry;  formerly  Physician  to  the  Philadelphia 

Hospital;    Author   of  "Clinics  in  Optometry,"  etc. 

THE  OPTICIAN'S  ^lANUAL,  Vol  I,  is  the  most 
popular  and  useful  work  on  practical  refraction 
ever  written,  and  has  been  the  entire  optical  edu- 
cation of  many  hundred  successful  refractionists. 
The  knowledge  it  contains  was  more  effective  in  building  up 
the  profession  of  optometry  than  any  other  educational 
factor.  It  is,  in  fact,  the  foundation  structure  of  all  op- 
tometric  knowledge  as  the  titles  of  its  ten  chapters  show : 

Chapter  I.— Introductory  Remarks. 
Chapter  II.— The  Eye  Anatomically. 
Chapter     III.— The  Eye  Optically;  or, 

The  Physiology  of  Vision. 
Chapter    IV.— Optics. 
Chapter      V.— Lenses. 
Chapter    VI. — Numbering  of  Lenses. 
Chapter   VII. — The  Use  and  Value  of  Glasses. 
Chapter  VIII.— Outfit  Required. 
Chapter     IX.— Method  of  Examination. 
Chapter      X. — Presbyopia. 

In  its  present  revised  and  enlarged  form  this  volume  is 
the  recognized  standard  text-book  on  practical  refraction, 
being  used  as  such  in  all  schools  of  Optics.  A  study  of  it 
is  essential  to  an  intelligent  appreciation  of  its  companion 
treatise,  The  Optician's  Alanual,  Vol.  II.  A  comprehensive 
index  adds  much  to  its  usefulness  to  both  student  and 
practitioner. 

Bound  in  cloth — 422  pages— colored  plates  and  illustrations. 
Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.50 

Published  by 
THE   KEYSTONE   PUBLISHING   COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


The  Optician's  Manual 

VOL.  II. 

By  C.  H.  BROWN,  M.D. 

Graduate  University  of  Pennsylvania  ;  Professor  of  Optics  and  Refraction  ; 

Formerly  Physician  in  Philadelphia  Hospital ;  Author  of  "Clinics  in 

Optometry  ";  "  State  Board  Questions  and  Answers  ";  Etc. 

THE  Optician's  Manual,  Vol,  II.,  is  a  direct 
continuation  of  The  Optician's  Manual,  Vol,  I., 
being  a  much  more  advanced  and  compre- 
hensive treatise.  It  covers  in  minutest  detail 
the  four  great  subdivisions  of  practical  eye  refraction,  viz  : 

MYOPIA 

HYPERMETROPIA 
ASTIGMATISM 
MUSCULAR  ANOMALIES 

It  contains  the  most  authoritative  and  complete 
researches  up  to  date  on  these  subjects,  treated  by  the 
master  hand  of  an  eminent  oculist  and  optical  teacher. 
It  is  tlioroughly  practical,  explicit  in  statement  and 
accurate  as  to  fact.  All  refractive  errors  and  complica- 
tions are  clearly  explained,  and  the  methods  of  correc- 
tion thoroughly  elucidated. 

This  book  fills  the  last  great  want  in  higher  refrac- 
tive optics,  and  the  knowledge  contained  in  it  marks 
the  standard  of  professionalism. 

Bound  in  Cloth.  408  pages,  with  illustrations. 

Sent  postpaid  to  any  part  of  the  -world  on  receipt  of  price 

$2.50 


Published  by 
THE  KEYSTONE  PUBLISHING  COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


Clinics  in  Optometry 

By  C.  H.  BROWN,  M.  D. 

Graduate  University  of  Pennsylvania:  Professor  of  Principles  and 

Practice  of  Optonu'try  ;  formerly  Physician  to  the 

Philadelphia  Hospital;   Author  of  the 

Optician's  Manual,  Etc. 


CLINICS  IN  OPTOMETRY"  is  a  unique 
work  in  the  field  of  practical  refraction  and 
fills  a  want  that  has  been  seriously  felt  both 
by  oculists  and  optometrists. 
The  book  is  a  compilation  of  optonietric  clinics,  each 
clinic  being  complete  in  itself.  Together  they  cover 
all  manner  of  refractive  eye  defects,  from  the  simplest 
to  the  most  complicated,  giving  in  minutest  detail  the 
proper  procedure  to  follow  in  the  diagnosis,  treatment 
and  correction  of  all  such  defects. 

Practically  everv  case  that  can  come  before  you 
is  thoroughly  explained  in  all  its  phases  in  this  useful 
volume,  making  mistakes  or  oversights  impossible  and 
assuring  correct  and  successful  treatment. 

The  author's  experience  in  teaching  the  science  of 
refraction  to  thousands  of  pupils  peculiarly  equipped 
him  for  compiling  these  clinics,  all  of  which  are  actual 
cases  of  refractive  error  that  came  before  him  in  his 
practice  as  an  oculist. 

A  copious  index  makes  reference  to  any  particular 
case,  test  or  method,  the  work  of  a  moment. 

BOUND   IN   SILK   CLOTH 
Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.50 


Published  by 
THE  KEYSTONE   PUBLISHING   COMPANY 

P.O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


Tests  and  Studies 

of  the  Ocular 

Muscles 

By  ERNEST  E.  MADDOX,  M.D.,  F.R.C.S.,  Ed. 

Ophthalmic  Surgeon  to  the  Royal  Victoria  Hospital,  Bournemouth,  Engfland  ; 
formerly  Syme  Surgical  Fellow,  Edinburgh  University 

THIS  book,  is  universally  recognized  as  the 
standard  treatise  on  the  muscles  of  the  eye, 
their  functions,  anomalies,  insufficiencies,  tests 
and  optical  treatment. 
All  optometrists  recognize  that  the  most  troublesome 
subdivision  of  refractive  work  is  muscular  anomalies. 
Even  those  who  have  mastered  all  the  other  intricacies 
of  visual  correction  will  often  find  their  skill  frustrated 
and  their  efforts  nullified  if  they  have  not  thoroughly 
mastered  the  ocular  muscles. 

The  eye  specialist  can  thoroughly  equip  himself 
in  this  fundamental  essential  by  studying  the  work  of 
Dr.  Maddox,  who  is  known  in  the  world  of  medicine 
as  the  greatest  investigator  and  authority  on  the  sub- 
ject of  eye  muscles. 

The  present  volume  is  the  second  edition  ot  the 
work,  specially  revised  and  enlarged  by  the  author.  It 
is  copiously  illustrated  and  the  comprehensive  index 
greatly  facilitates  reference. 

Bound   in   Silk   Cloth  —  261  Pages  —  110  Illustrations. 
Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.50 

J* 

Published  by 

THE  KEYSTONE  PUBLISHING   COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


Physiologic  Optics 

Ocular  Dioptrics  — Functions  of  the 

Retina  —  Ocular  Movements  and 

Binocular  Vision 

By   DR.   M.   TSCHERNING 

Director  of   the    Laboratory  of    Ophthalmology 
at  the  Sorbonne,  Paris 

AUTHORIZED   TRANSLATION 

By  CARL  WEILAND,  M.D. 

Former  Chief  of  Clinic  in  the  Eye  Department  of  the 
Jefferson  College  Hospital,  Philadelphia,  Pa. 

THIS  book  is  recognized  in  the  scientific  and  medical 
world  as  the  one  complete  and  authoritative  treatise 
on  physiologic  optics.  Its  distinguished  author  is 
admittedly  the  greatest  authority  on  this  subject, 
and  his  book  embodies  not  only  his  own  researches,  but  those 
of  the  several  hundred  investigators  who,  in  the  past  hundred 
years,  made  the  eye  their  specialty  and  life  study. 

Tscherning  has  sifted  the  gold  of  all  optical  research 
from  the  dross,  and  his  book,  as  now  published  in  English, 
with  many  additions,  is  the  most  valuable  mine  of  reliable 
optical  knowledge  within  reach  of  ophthalmologists.  It  con- 
tains 380  pages  and  212  illustrations,  and  its  reference  list 
comprises  the  entire  galaxy  of  scientists  who  have  made 
the  century  famous  in  the  world  of  optics. 

The  chapters  on  Ophthalmometry,  Ophthalmoscopy, 
Accommodation,  Astigmatism,  Aberration  and  Entoptic 
Phenomena,  etc. — in  fact,  the  entire  book  contains  so  much 
that  is  practical  and  necessary,  that  no  refractionist  can 
afford  to  be  without  it. 

Bound  in  Cloth.  380  Pages,  212  Illustrations. 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$3.00 

A* 

Published  by 
THE  KEYSTONE  PUBLISHING  COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


The  Refractive  and 

Motor  Mechanism 

of  the  Eye 

By  WILLIAM  NORWOOD  SOUTER,  M.D. 

Associate  OphthalmoloRist,  Episcopal  Eye,  Ear 
and  Throat  Hospital,  Washington,  D.  C. 

THIS  work  by  one  of  the  most  eminent  ophthal- 
mologists in  the  United  Sta,tes,  brings  the 
science  of  eye  refraction  right  up  to  date  and 
embodies,  in  addition  to  the  profound  knowledge  of 
the  author,  all  the  researches  on  the  subject  that  experi- 
ence has  established  as  authoritative. 

The  geometric  and  mathematical  optics  on  which 
the  principles  of  optometry  are  based,  necessary  infor- 
mation to  optical  stttdents  of  to-day,  will  be  found  in 
simplified  form  in  the  Appendix  of  this  treatise. 

Students,  teachers  and  practitioners  alike,  in  study- 
ing this  book  or  using  it  for  reference,  have  the  assur- 
ance of  absolute  reliability  of  statement  and  complete 
elimination  of  the  misleading  fallacies  which  mar  the 
worth  of  many  works  on  this  subject. 

It  contains  350  pages  with  148  illustrations,  many 
entirely  original,  and  is  probably  the  only  scientific 
work  ever  published  in  which  every  single  reference 
was  verified  absolutely  by  the  author  himself 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.50 

J* 

Published  by 

THE  KEYSTONE   PUBLISHING   COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


Ophthalmic  Lenses 

Dioptric  Formulae  for  Combined  Cylindrical 

Lenses,  The  Prism-Dioptry  and 

Other  Original  Papers 

By  CHARLES  F.  PRENTICE,  M.E. 

A  new  and  revised  edition  of  all  the  original  papers  of  this  noted  author, 
combined  in  one  volume.  In  this  revised  form,  with  the  addition  of  recent 
research,  these  standard  papers  are  of  increased  value.  Combined  in  one 
volume,  thev  are  the  greatest  compilation  on  the  subject  of  lenses  extant. 
This  book  of  over  200  pages  contains  the  following  papers: 

Ophthalmie  Lenses. 

Dioptric  Formulae  for  Combined  Cylindrical  Lenses. 

The  Prism-Dioptry. 

A  Metric  System  of  Numbering  and  Measuring  Prisms. 

Tlie  Uelaliou  of  the  Prisiii-Uioptry  to  the  Meter  .Angle. 

The  delation  of  the  Prisni-I)ioiJIry  to  the  Leus-Diojitry. 
The  Perfected  Prismometer. 
The  Prismometric  Scale. 
On  the  Practical  Execution  of  Ophthalmic  Prescriptions 

involving  Prisms. 
A  Problem  in  Cemented  Bi-Focal  Lenses,  Solved  by  the 

Prism-Dioptry. 
Why  Strong  Contra-Generic  Lenses  of  Equal  Power  Fail 

to  Neutralize  Each  Other. 
The  Advantages  of  the  Sphero-Toric  Lens. 
The  Iris,  as  Diaphragm  and  Photostat. 
The  Typoscope. 
The  Correction  of  Depleted  Dynamic  Refraction  (Presbyopia). 

PRESS  NOTICES  OF  THE  ORIGINAL  EDITION: 

OPHTHALMIC  LENSES 

"The  work  stands  alone,  in  its  present  form,  a  compendium  of  the  various  laws  of 
physics  relative  to  this  subject  that  are  so  difficult  ot   access  in  scattered  treatises." 

— New  E>igland  Medical  Gazette. 

"  It  is  the  most  complete  and  best  illustrated  book  on  this  special  subject  ever  published." 

—Horohgical  Review,  New  York. 

"Of  all  the  simple  treatises  on  the  properties  of  lenses  that  we  have  seen,  this  is  incom- 
parably, the  best.  .  .  .  The  teacher  ot  the  average  medical  student  will  hail  this 
little  work  as  a  great  boon."        — Archives  of  Ojjfithalmology,  edited  hy  H.  Knapp,  M.D. 

Bound  in  Silk  Cloth.  110  Original  Diagrams. 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.00 

J* 

Published  by 
THE   KEYSTONE   PUBLISHING   COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


The  Making  of  a 

Mechanical 

Optician 

A  PRACTICAL  TREATISE  ON  THE  MECHANICAL 
WORK  OF  OPTOMETRISTS  AND  OPTICIANS 

By  W.  W.  SLADE 

Of  the  Globe  Optical  Company,  Boston,  Mass. 

THIS  new  volume  is  the  only  treatise  published 
on  mechanical  optics  with  special  reference  to 
the  work  of  optometrists  and  opticians.  The 
author  is  regarded  in  the  optical  world  as  the 
highest  authority  on  this  important  branch  of  optical  prac- 
tice, and  his  reputation  is  an  assurance  to  the  trade  of  the 
absolute  reliability  of  the  work. 

The  seventeen  chapters  of  the  new  work  cover  thor- 
oughly all  the  mechanical  operations  of  the  optician  from  in- 
forming him  as  to  the  machinery  needed  and  the  handling 
of  tools,  to  the  final  operation  in  the  correct  filling  of 
prescriptions  and  the  production  of  first-class  optical  work. 
There  are  chapters  on  lens  marking  and  cutting,  lens  grind- 
ing, drilling  and  mounting,  bifocal  work,  soldering,  repair- 
ing, bridge  bending,  surface  grinding,  etc.,  etc. 

The  illustrations  are  in  greater  part  entirely  original 
and  were  especially  executed  for  the  purposes  of  this 
volume.  These  add  greatly  to  the  instructive  character  of 
the  book,  which  is  indispensable  to  every  optometrist  and 
optician. 

Send  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.50 


Published  by 

THE  KEYSTONE  PUBLISHING  COMPANY 

p.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


Record-Book  of 
Optometric 
Examinations 

j4  RECORD-BOOK,  wherein  to  record  opto- 
/  ^  metric  examinations,  is  an  indispensable  ad- 
/      ^^junct  to  an  optometrist's  outfit. 

The  Keystone  Record-Book  of  Optometric  Exami- 
nations w-:s  specially  prepared  for  this  purpose.  It 
excels  all  others  in  being  not  only  a  record-book,  but 
an  invaluable  guide  in  examination. 

The  book  contains  two  hundred  record  forms  with 
printed  headings,  suggesting,  in  the  proper  order,  the 
course  of  examination  that  should  be  pursued  to  obtain 
most  accurate  results. 

Each  book  has  an  index,  which  enables  the  optom- 
etrist to  refer  instantly  to  the  case  of  any  particular 
patient. 

The  Keystone  Record-Book  diminishes  the  time 
and  labor  required  for  examinations,  obviates  possible 
oversights  from  carelessness,  and  assures  a  systematic 
and  thorough  examination  of  the  eye,  as  well  as 
furnishing  a  permanent  record  of  all  examinations. 

Sent  postpaid  to  any  part  of  the  world  on  receipt  of  price 

$2.00 


Published  by 
THE  KEYSTONE   PUBLISHING   COMPANY 

P.  O.  BOX  1424  PHILADELPHIA,  U.  S.  A. 


16  7905-^ 


■oy. 


.^^' 


% 


p7^ 


./ 


^4^ 
^ 


^ 


'^ 


^ 


% 


.♦ 


'^> 


^^^ 


^ 


^^, 


"%5 


^^ 


A^^ 


^<^/. 


fe.     .<i»^ 


.<5.^^ 


0       % 


% 


^^ 


.# 


^ 


RETURN    OPTOMETRY  LIBRARY 
jOhm^    490  Minor  Ha" 


LOAN  PERIOD  1 

HOMiE  USE 


2 


642-1020 


-      I? 


ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS 
RENEWALS  MAY  BE  REQUESTED  BY  PHONE 


DUE  AS  STAMPED  BELOW 


Mc^u^l 


MAYa^-f985 


—      />- 


DK.  18  1992, 


^  1996 


..-^ 


^^ 


UNIVERSITY  OF  CALIFORNIA,  BERKELEY 
FORM  NO.  DD  23,  2.5m,  12/80    BERKELEY,  CA  94720 


% 


^ 


.^^ 


^ 


